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S0973082620303112
Stove and fuel stacking is becoming accepted as part of the clean cooking transition process even though it attenuates positive health and climate benefits that can be realized by cookstove interventions . This study analyses the underlying drivers of stove and fuel stacking from the household perspectives and its implications for improving impact of clean cooking programs .
We use a qualitative study design to generate explanations why stove and fuel stacking is pervasive in three Kenyan settings. The explanations coalesce around the need for simultaneous cooking and practical limitations of the new technologies. Fuel availability cost and tenancy arrangements also emerge as important for urban residents. Preference for food prepared on certain stoves did not emerge as an important reason for stacking. Offering a range of clean stacking solutions can support the transition process towards clean cooking.
S0973082620303124
This study uses a static computable general equilibrium model to examine the potential economic impacts of ethanol production in Uganda . We introduce an ethanol sector in the 2016 17 Uganda s social accounting matrix using maize cassava sugarcane and molasses as feedstocks . Furthermore we evaluate the suitability of each feedstock . By simulating a 10 blending mandate we find that factor employment and total output would increase with a sluggish rise in commodity prices . Real GDP would grow moderately and household income increase mostly for the rural households . Household welfare would decline because of a counter financing tax on gasoline . A reduction in gasoline imports is likely to improve the trade balance and despite the ensuing decline in import tax revenues government income would still rise . Our results are suggestive of ethanol production as a potential pro poor project for Uganda . Both sugarcane and maize are more growth enhancing compared to cassava . The use of only molasses from the sugar industry may result in negative impacts since it is already an input in other activities . We also observe that using an average of multiple feedstocks would be more sustainable . Moreover it would allow a more balanced growth while reducing upward price pressures .
We model the potential impacts of ethanol production in Uganda using a static CGE. Ethanol is a potential pro poor project as reflected by the growth in household income. There are high prospects of an improved trade balance from promoting ethanol. An average of multiple feedstocks would be more sustainable.
S0973082620303136
Water heating represents a large fraction of energy consumption in the residential sector and it has significant health economic and environmental implications . However it is well known that temperatures between 20C and 42C promote the multiplication of
Point of Use Water Heating cannot compete economically against Gas Water Heating. Point of Use Water Heating prevents from Legionella in continental climates. Point of Use Water Heating uses less energy than Electric Storage type Heating.
S0973082620303148
The transport sector has become an important source of urban greenhouse gas and air pollutant emissions with the continuous growth of transportation demand . The co benefits of reducing GHG and air pollutant emissions in the transport sector are receiving more and more attention . Taking Guangzhou as the case study city this study quantitatively analyzed the co benefits of reducing CO
The entire urban transport sector is taken as the research object. The co benefits of reducing CO. and pollutant emissions are quantitatively analyzed. Adjusting transport modes and electrification have significant co benefits. Increasing the application of bio fuel and hydrogen energy also has good co benefits. Promoting the utilization of LNG vehicles and ships has poor co benefits.
S0973082620303161
Knowledge on the effects of climate change in a system can contribute to the better management of its water and energy resources . This study evaluates the consequences of alterations in the rainfall and temperature patterns for a hydroelectric plant . The methodology adopted consists of four steps . First a hydrological model is developed for the chosen basin following a semi distributed and conceptual approach . The hydrological model is calibrated utilizing the optimization algorithm Shuffled Complex Evolution University of Arizona and then validated . Secondly a hydropower model is developed for a hydroelectric plant of the chosen basin . The hydropower model is adjusted to the physical characteristics of the plant . Thirdly future climate scenarios are extracted from the literature for the studied area . These scenarios include quantitative and seasonal climate variations as well as different initial reservoir levels . Fourth the hydrological hydropower model is simulated for 52 scenarios and the impact of changes in the rainfall and temperature patterns for hydropower generation is evaluated . For each scenario the water storage in the reservoir and energy produced by the plant are analyzed . The financial impact for extreme scenarios is presented . The methodology is applied to the Trs Marias hydroelectric plant at the upper So Francisco river basin and it can be replicated to any other hydropower system . The results show that extreme positive values predicted for rainfall will likely not cause issues to the plant considering a moderate rise in temperature . However negative predictions for rainfall regardless of changes in temperature should be an alert to the authorities responsible for water and energy resources management .
The consequences of climate change for hydropower generation are evaluated. A hydrological hydropower model is developed for the studied area. The water storage and generated power are analyzed for 52 climate scenarios. Wet scenarios with a moderate rise in temperature are positive for the plant. Decrease in rainfall independent of the temperature compromise the plant operation.
S0973082620303173
Located deep in the Kelabit Highlands in Malaysian Borneo the remote town of Bario offers us a natural laboratory of rural electrification projects through which to understand end user perceptions of success and failure and the factors that contribute to these perceptions . We use a case study based approach and focus on three off grid energy projects a 110kW mini hydro power plant a 12kW wind turbine system and a 1.59MW solar diesel hybrid system . We find that end users primarily see the success or failure of a project in technical terms but that this narrow conceptualization masks important interactions between technical economic and institutional factors . We further find that end user perceptions of newer projects are heavily affected by their perceptions of previous projects . Our findings suggest several ways forward to improve the effectiveness of rural electrification initiatives . Firstly we should expect complex interactions between technical economic and institutional factors and build in the necessary capacity into rural electrification projects to identify and address these interactions . Secondly there is no one size fits all solution to creating the requisite capacity to deal with interactions among technical economic and institutional factors . Thirdly ongoing qualitative or mixed methods evaluations of rural electrification initiatives can help unravel what would otherwise be hidden interactions between technical economic and institutional factors .
We qualitatively evaluate off grid projects from the perspective of end users. Outcomes are shaped by complex technical economic and institutional interactions. Perceptions of newer projects are heavily affected by past experiences of failure. Qualitative studies can identify and address hidden barriers to electrification.
S0973082620303185
The rural electrification based literature reports a limited modelling knowledge concerning the long term dynamics of the nexus between electricity access and local development in rural areas of developing countries . This can hinder the achievement of the Agenda 2030 goals related to sustainable access to electricity for all . In order to overcome this literature gap and support the implementation of sustainable long term rural electrification programmes this paper builds upon the research on a system dynamics model on the local dimension of the electricity development nexus developed by the authors by testing it and deriving useful guidelines for supporting future electrification actions in sub Saharan Africa . All the steps are based on a real case study as reference i.e . a hydroelectric based electrification programme implemented in the rural community of Ikondo Tanzania in 2005 by the Italian NGO named CEFA Onlus . The results of the model testing lead to a novel quantitative assessment of the most relevant dynamics affecting the local electricity development nexus and it provides a novel discussion on model results when its inputs take on different values until the extreme ones and as if the model were tested for different contexts than Ikondo . Policy testing is also performed for exploring model behaviour when subjected to different polices and exogenous decision making processes . It provides a list of complementary activities to couple with electrification programmes for enhancing their positive impact on rural communities . These results can support the definition of useful guidelines and best practices for rural electrification in sub Saharan Africa and they advocate an updating of the traditional monitoring and evaluation frameworks commonly used for assessing energy access projects .
A system dynamics model on the electricity development nexus is tested. A novel assessment of the dynamics affecting the rural electricity development nexus is provided. Useful lessons learnt for supporting future electrification actions in sub Saharan Africa are reported. Complementary activities to couple with electrification programmes are discussed.
S0973082620303197
This paper analyzes the effects of the 9 min pan India voluntary lights off policy that was planned and executed by the Government of India in April 2020 on the National Grid and the steps that were taken to maintain grid stability during the event . The policy was a symbolic gesture of public solidarity with frontline healthcare and emergency workers in the nation s war against the COVID 19 pandemic . The event entailed nationwide switching off of electric lights and lighting of earthen lamps or switching on of torch lights . This 9 min event posed a significant challenge to the country s power systems engineers in managing grid stability during the large scale load reduction and meticulous planning and implementation of protective measures were carried out . In this article the strategy implemented by the Indian power sector to manage the grid during the nine minute event is described . The variations of grid parameters such as frequency voltage and load at all dispatch centers before during and after the nine minutes are analyzed and the generation schedule that was followed is also presented along with real time results . This case study provides an overview of power systems management that involves strategic scheduling of generators throughout the country to tackle sudden and mass reductions of load on the power system .
Covid 19 and its impact on the world. History of blackouts and brownouts brownouts in a power system. Overview of the India power system and national power grid development. Pan India lights off policy on 5. April 2020. Power system operation and control during an emergency
S0973082620303203
This research assesses the transition of a fossil fuel based electricity production jurisdiction to a renewable based electricity jurisdiction through an extensive scenario analysis . This fills a knowledge gap where a wide range of fossil to renewable electricity generation pathways is compared within a single analysis framework . To conduct this study a novel data intensive electricity system model was developed with the Long range Energy Alternatives Planning system and applied to evaluate alternative electricity generation mix scenarios to the year 2050 . A case study for Alberta a fossil fuels based province in Canada was conducted . A total of 382 scenarios were analyzed considering different renewable pathways and varying key uncertain future conditions . The greenhouse gas emission abatement and marginal greenhouse gas abatement costs of each scenario were evaluated and compared . Several renewable based scenarios resulted in significant greenhouse gas abatement at lower costs than the fossil fuel based business as usual scenario . The maximum greenhouse gas abatement possible at a net cost reduction compared to the business as usual scenario was found through a specific combination of wind hydro and solar power which resulted in over a 90 reduction from 2005 emission levels at 1.8 t of carbon dioxide equivalent abated . The results of this study provide policy insight for jurisdictions transitioning away from fossil fuel based electricity to renewables .
A new Long range Energy Alternatives model is developed and applied. Extensive analysis of energy transition for a fossil fuel electricity sector. 382 scenarios representing different technology mixes and assumptions are evaluated. Highly renewable technology mixes offer system cost savings compared baseline. Over 90 greenhouse gas mitigation technically and economically feasible.
S0973082620303215
In Tanzania fuelwood availability for cooking is an increasing challenge for rural households struggling to meet this need . Here a possible pathway for smallholder farmers to reduce their dependency on off farm fuelwood is evaluated . We compare the cooking performance of on farm produced fuels like wood from
Selected on farm fuels perform better than off farm fuels during cooking. Improved Cooking Stoves do not always outperform Three Stone Fire stoves. Energy and time saved during cooking depend on the type of cooking task. On farm fuels and Improved Cooking Stoves add to household fuel sovereignty. Pigeon pea stalks are a suitable addition to the household energy mix.
S1007570419301765
Since impulsive control has less conservation in the analysis of dynamical behaviors a surge of attention has been paid on the study of impulsive control systems . This paper is dedicated to review some recent developments of impulsive control theory . Some fundamental theory on impulsive control systems and some very recent interesting results are reviewed and addressed . Based on the characteristics of impulsive control systems we summarize three fundamental factors for the design of impulsive controllers namely the impulsive strength the impulsive frequency and the impulsive instant . Then a systematic account of useful stability analysis methods are introduced and these methods provide researchers a well organized tool box to learn the impulsive control systems . Moreover as a vital aspect the effects of delays on impulsive systems are discussed . Finally some potential developments and further work on impulsive control systems are briefly presented and discussed .
Some fundamental results on impulsive control systems and recent research work are here reviewed and addressed. We summarize three fundamental factors for the design of impulsive controllers namely the impulsive strength the impulsive frequency and the impulsive instants. Some potential development and some further work on impulsive control systems are briefly presented and discussed.
S1007570419301868
In this paper transient influence of correlation between external and parametric excitations on system response is investigated . Time variable has been taken into account . This does not seem to have been studied previously . By describing correlation between excitations quantitively with correlated coefficient general Fokker Planck Kolmogorov equation is reformulated with two parts . The first part relates to the one of independent excitations while the other part is caused by the correlated excitations . Then exponential polynomial closure method by taking time variable into account is further developed for transient responses of nonlinear oscillators under correlated excitations . With the improved EPC method typical system of Duffing oscillator under correlated external and parametric Gaussian white noise excitations is investigated . Based on the results it is found the influence of correlation between excitations on system response depends directly on the magnitude and the sign of the correlation coefficient . Besides the influence seems stationary and not affected by the time . In addition the results obtained from the EQL method are not consistent with the actual ones with unsymmetrical PDFs and nonzero means . It is indicated that the EQL method is not applicable to such case .
Comparisons between solutions and computational time evidence that the developed EPC method is an effective and efficient method. The influence of correlation between excitations on system responses depends directly on the correlation coefficient. The influence of correlation between excitations on system response seems stationary and not affected by the time. When the external and parametric excitations are correlated the EQL method is not applicable since it does not reflect properties of system responses with unsymmetrical PDFs and nonzero means especially for velocity response.
S1007570419302242
Starting from the RiemannLiouville derivative many authors have built their own notion of fractional derivative in order to avoid some classical difficulties like a non zero derivative for a constant function or a rather complicated analogue of the Leibniz relation . Discussing in full generality the existence of such operator over continuous functions we derive some obstruction Lemma which can be used to prove the triviality of some operators as long as the linearity and the Leibniz property are preserved . As an application we discuss some properties of the Jumaries fractional derivative as well as the local fractional derivative . We also discuss the chain rule property in the same perspective .
The Leibniz and chain rule properties are discussed in the light of various extensions of the RiemannLiouvile fractional derivative. We derive the obstruction Lemma and use it to prove the triviality of some fractional operators defined on continuous functions as long as the linearity and the Leibniz property are preserved. We explain that the operator which satisfies the chain rule property and is zero on a constant function needs to be trivial. The Jumaries fractional derivative and the local fractional derivative proposed by Kolwankar and Gangal are discussed as examples.
S1007570419302485
In this paper we investigate the inverse scattering transforms and soliton solutions of both focusing and defocusing Hirota equations with non zero boundary conditions . The inverse problems are solved via the study of the matrix Riemann Hilbert problems . As a consequence we present the general solutions for the potentials and explicit expressions for the reflectionless potentials . Moreover the trace formulae and theta conditions are also given . Particularly we discuss the simple pole and double pole solutions for the focusing case and the simple pole solutions for the defocusing case . Moreover the results of the focusing case with NZBCs can reduce to ones of the focusing case with zero boundary condition . These obtained solutions are useful to explain the related nonlinear wave phenomena .
The inverse scattering transforms of both focusing and defocusing Hirota equations with non zero boundary conditions NZBCs are found. The inverse problems are solved via the study of the matrix Riemann Hilbert problems. We present the general solutions of the potentials and explicit expressions for the reflectionless potentials. The trace formulae and theta conditions are given. The simple pole and double pole solutions for the focusing case and the simple pole solutions for the defocusing case are found.
S1007570419302564
Transport in Hamiltonian systems with weak chaotic perturbations has been much studied in the past . In this paper we introduce a new class of problems transport in Hamiltonian systems with slowly changing phase space structure that are not order one perturbations of a given Hamiltonian . This class of problems is very important for many applications for instance in celestial mechanics . As an example we study a class of one dimensional Hamiltonians that depend explicitly on time and on stochastic external parameters . The variations of the external parameters are responsible for a distortion of the phase space structures chaotic weakly chaotic and regular sets change with time . We show that theoretical predictions of transport rates can be made in the limit where the variations of the stochastic parameters are very slow compared to the Hamiltonian dynamics . Exact asymptotic results can be obtained in the one dimensional case where the Hamiltonian dynamics is integrable for fixed values of the parameters . For the more interesting chaotic Hamiltonian dynamics case we show that two mechanisms contribute to the transport . For some range of the parameter variations one mechanism called transport by migration with the mixing regions is dominant . We are then able to model transport in phase space by a Markov model the local diffusion model and to give reasonably good transport estimates .
Transport in Hamiltonian systems with slow stochastic parameters is the result of two different mechanisms which we characterize. We provide an asymptotically exact stochastic equation for long term transport of action variables when the Hamiltonian is integrable. When the Hamiltonian is chaotic we show using averaging that long term transport is equivalent to a simple Markov process.
S1007570419302679
This paper is concerned with robust stabilization problem of TakagiSugeno fuzzy time delay systems subject to impulsive perturbations . New results on robust stabilization via parallel distributed compensation control are derived . First based on the impulse type RazumikhinLyapunov method combined with the use of an impulse time dependent Lyapunov function a new exponential stability criterion for T S fuzzy time delay system with impulsive effects is obtained . The proposed stability criterion removes the restrictive condition on the relationship between the size of time delay and lower bound of impulse intervals imposed by the previous results . Then by employing a convex relaxation technique a sufficient condition for the constructing the PDC controllers is presented which is expressed in terms of linear matrix inequalities . Next the robust stabilization problem for the T S system with slowly time varying delay is studied . A different stabilization condition is derived via an impulse time dependent Lyapunov functional which is less conservative than the former when the state delay is constant . Finally an illustrative example is provided to demonstrate the effectiveness of the proposed analysis and design techniques .
New analysis and design methods based on the use of impulse time dependent Lyapunov function functional are proposed. The restrictive condition on the relationship between the size of time delay and lower bound of impulse intervals imposed by the previous results is removed. The fuzzy PDC control design methodology for both cases of fast and slow time varying delay is developed.
S1007570419302709
This paper is concerned with the problem of finite time stable walking for a 5 link under actuated biped robot . Due to instantaneous change of 2 legs and complex dynamics during the walking process the robot can be regarded as a nonlinear impulsive system . In order to make impulsive control of the robotic system it is modeled as a rigid kinematic chain with Lagrange equations which is strong coupling and hybrid . A novel finite time feedback controller is proposed to realize finite time stability of the nonlinear impulsive system . The controller is designed based on finite time stabilizing control Lyapunov function and hybrid zero dynamics . By establishing a finite time stable periodic orbit the controller can make the output of virtual constraints converge to zero rapidly . Restricted Poincare return map is then utilized to analyze the finite time stability of nonlinear impulsive system . It ensures that the flow of the continuous subsystem can pass through the impact cross section . Additionally a periodic walking gait planning is further investigated and the existence of the gait is proved which satisfy the joint trajectory tracking . Finally the effectiveness of the mentioned method is illustrated by simulations .
A finite time stable feedback controller based on finite time stabilizing control Lyapunov function. Restricted Poincare return map and hybrid zero dynamics for the finite time stability of hybrid system. A finite time stable periodic walking gait planning and its existence.
S1007570419302710
In this paper we consider the problem of existence of almost periodic solutions of impulsive CohenGrossberg neural networks with time varying delays . The impulses are not at fixed moments but are realized when the integral curves of solutions meet given hypersurfaces i.e . the investigated model is with variable impulsive perturbations . Sufficient conditions for perfect stability of almost periodic solutions are derived . The main results are obtained by employing the LyapunovRazumikhin method and a comparison principle . In addition the obtained results are extended to the uncertain case and robust stability of almost periodic solutions is also investigated . An example is considered to demonstrate the effectiveness of our results .
A class of Cohen Grossberg neural networks is investigated. We establish criteria for existing of almost periodic solutions. Variable impulsive perturbations and time varying delays are considered. The Lyapunov function method and Razumikhin principle are applied. Global perfect stability behavior of the solutions is discussed.
S1007570419302722
In this paper we derive and analyze a reaction diffusion cholera model in bounded spatial domain with zero flux boundary condition and general nonlinear incidence functions . The parameters in the model are space dependent due to the spatial heterogeneity . By applying the theory of monotone dynamical systems and uniform persistence we prove that the model admits the global threshold dynamics in terms of the basic reproduction number
A diffusive cholera model with general incidence functions is studied. The threshold property of the basic reproduction number R0 is established. Cholera cannot be controlled only by limiting the movement of host individuals. The spatial heterogeneity does not always enhance the disease spread.
S1007570419302746
Stochastic models for hepatitis C virus infection based on the dynamics of a deterministic model incorporating both modes of infection transmission and antibody response with the consideration of natural cure of infected hepatocytes are developed and analyzed . In the model formulation the two processes for the release of virions namely budding and bursting are assumed . The It stochastic differential equation models for both budding and bursting processes with fixed as well as variable burst size are constructed using the property of linear transformation for multivariate normal distribution and the continuous time Markov chain models utilizing the theory of multitype continuous time branching process in its derivation . The stochastic means with standard deviations for the SDE model variables are numerically calculated and graphically compared with the results from the deterministic model . The findings suggest that the probability of virus extinction estimated from the CTMC models is not only dependent on the case whether the basic reproduction number is greater than unity but it also depends on the initial viral load . The probability of virus extinction is comparatively higher in case of budding than in case of bursting . Furthermore the forward Kolmogorov and moment equations corresponding to the SDE models for both budding and bursting are derived and numerically illustrated with a particular case .
Stochastic models for hepatitis C virus HCV dynamics are proposed. Bursting and budding are used to model the release of HCV. Probability of virus extinction depends on initial level of virions and infection.
S1007570419302758
We consider a version of the ultimatum game which simultaneously combines reactive and Darwinian aspects with offers in . By reactive aspects we consider the effects that lead the player to change their offer given the previous result . On the other hand Darwinian aspects correspond to copying a better strategy according to best game payoff when the current player compares with one of their neighbours . Therefore we consider three different strategies which govern how the players change their offers greedy moderate and conservative . First we provide an analytic study of a static version of game where Darwinian aspects are not considered . Then by using numerical simulations of a detailed and complete multi agent system on a two dimensional lattice we add an extra feature in which players probabilistically escape from extreme offers for obvious reasons . The players are also endowed reciprocity on their gains as proposers which is reflected on their gains as responders . We also analyse the influence of the players mobility effects . An analysis of the emergence of coexistence of strategies and changes on the dominant strategies are observed which in turn depends on the players mobility rate .
Ultimatum game is considered in a version that mixes reactive and Darwinian aspects. Players that moderate their greedy dominate the population in high diffusion. Numerical results are studied considering a suitable Multi agent system. Analytical results deduce how the portfolios can lead to the fairness.
S1007570419302898
Hysteresis is a special type of behavior ubiquitous in science and engineering it consists in that slow inputs produce a loop in the steady state part of the graph output versus input .
Mathematical textbooks on hysteresis use rate independence to define hysteresis processes. Experimental evidence shows that rate independence is but an approximation of real hysteresis systems. We propose a mathematical framework in which we can study a class of hysteresis systems that are not rate independent.
S1007570419302928
A recently proposed phase space boundary integral model for the stochastic propagation of ray densities is presented and for the first time explicit connections between this model and parametric uncertainties arising in the underlying physical model are derived . In particular an asymptotic analysis for a weak noise perturbation of the propagation speed is used to derive expressions for the probability distribution of the phase space boundary coordinates after transport along uncertain and in general curved ray trajectories . Furthermore models are presented for incorporating geometric uncertainties in terms of both the location of an edge within a polygonal domain as well as small scale geometric fluctuations giving rise to rough boundary reflections . Uncertain source terms are also considered in the form of stochastically distributed point sources and uncertain boundary data . A series of numerical experiments is then performed to illustrate these uncertainty models in two dimensional convex polygonal domains .
A boundary integral model for phase space densities including parametric uncertainties arising in an underlying ray tracing model. An asymptotic analysis for a weak noise perturbation of the propagation speed. Implicit modelling of curved trajectories and uncertain boundary geometry.
S100757041930293X
The probability density function of the time variant extreme value process for structural responses is of great importance . Poisson white noise excitation occurs widely in practical engineering problems . The extreme value distribution of the response of systems excited by Poisson white noise processes is still not yet readily available . For this purpose in the present paper a novel method based on the augmented Markov vector process for the PDF of the time variant extreme value process for a Poisson white noise driven dynamical system is proposed . Specifically the augmented Markov vector process is constructed by combining the extreme value process and its underlying response process . Then the joint probability density of the AMV can be evaluated by solving the Chapman Kolmogorov Equation e.g . via the path integral solution . Further the PDF of the time variant extreme value process is obtained and can be used say to estimate the dynamic reliability of a stochastic system . For the purpose of illustration and verification several numerical examples are studied and compared with Monte Carlo solution . Problems to be further studied are also discussed .
The time variant probability density function of extreme value of a system driven by Poisson white noise is studied. An augmented Markov vector process is constructed by combining the state vector and the extreme value process. A path integral solution with high efficiency is proposed. Several examples are illustrated demonstrating the effectiveness of the proposed method.
S1007570419302953
An American better of option is a rainbow option with two underlying assets . It can be described by a parabolic variational inequality on a two dimensional unbounded domain which can also be characterized by a two dimensional free boundary problem . Based on the numeraire transformation and the known information on the free boundary we derive a one dimensional linear complementarity problem related to options on a bounded domain . Moreover the full discretization scheme of LCP is constructed by finite difference and finite element methods in temporal and spatial directions respectively . The primal dual active set method is adopted for solving the resulting large scale discretized system . In each PDAS iteration a unique index set of primal dual variables will be computed by solving a linear system . A systematical convergent analysis is presented on our proposed method for pricing American better of options . One of the desirable features of our method is that we can get the option value and two free boundaries simultaneously . Numerical simulations are performed to verify the efficiency of our proposed method .
Based on the numeraire transformation and the known information on the free boundary we derive a one dimensional LCP related to the options on a bounded domain. To guarantee the accuracy around the singularity at the maturity time. we adopt the geometric partition instead of uniform partition inthe spatial direction. To get the option value and two free boundaries simultaneously we will use PDAS method to solve the LCP. Numerical simulations are performed to verifythe efficiency of our proposed method.
S1007570419302965
The classical master slave configuration allows synchronizing pairs of unidirectionally coupled systems or oscillators in a relatively easy manner . However it has been found that this scheme has a limitation for certain systemsincluding those with chaotic dynamicsthis scheme fails to induce synchronization . Consequently this paper focuses on deriving a potential solution for this limitation . In particular the manuscript presents a modified master slave scheme in which the static controller of the original scheme has been replaced by a first order dynamic controller . The stability of the synchronous solution is investigated by using the Lyapunov theory for perturbed systems and also by the well known Master Stability Function approach . Two application examples are considered namely synchronization of harmonic oscillators and synchronization of chaotic systems . For both examples a comparison between the performance of the classical scheme and the proposed configuration is provided . Additionally the proposed synchronization scheme is experimentally validated with electronic circuits which emulate the chaotic dynamics of Rssler system . Ultimately the results presented here show that the onset of synchronization in unidirectionally coupled systems is enhanced if the interaction between the systems is dynamic rather than static .
This work presents a modified master slave scheme in which the interaction between the master and slave is indirect via a dynamic coupling which is described by a first order linear system. The main advantage of the proposed scheme is that it can induce synchronization in the coupled systems even in the cases where the classical master slave scheme with static coupling fails to synchronize the systems. The stability of the synchronous solution in the modified master slave scheme is investigated by using Lyapunov theory for perturbed systems and the Master Stability Function approach. The performance of the proposed synchronization scheme is experimentally validated with electronic circuits.
S1007570419302977
In this article the viscously damped instability arising in the shear jet of west boundary layer governed by the two layer quasi geostrophic equation with a layered topography is analyzed . First the nonlinear stability and the exponential stability of the shear jet is studied . More precisely we derive an upper bound on the Reynolds number
We derive an upper bound on the Reynolds number below which the shear jet is globally exponentially stable. It is shown that under some boundedness condition on the steepness of the bottom topography and provided that the speed of the steady flow is sufficiently large and the viscosity is less than a threshold the shear jet will lose its stability. After the shear jet loses its stability then there exists a continuous transition in the west boundary layer and a stable periodic solution bifurcating from the shear jet. The stable periodic solution describes the observed circulation in ocean. It shows that the slope of the bottom has effect on the stability of the shear jet while it does not affect the transition type.
S1007570419302990
The well known nonlinear model for describing the solid tumour growth is under study using an approach based on Lie symmetries . It is shown that the model in the two dimensional approximation forms a dimensional boundary value problem which admits a highly nontrivial Lie symmetry . The special case involving the power law nonlinearities is examined in details . The symmetries derived are applied for the reduction of the nonlinear boundary value problem in question to problems of lower dimensionality . Finally the reduced problems with correctly specified coefficients were exactly solved and the exact solutions derived were analysed in particular some plots were build in order to understand the time space behaviour of these solutions and to discuss their biological interpretation .
It is proved that the tumour growth problem in question admits infinite dimensional Lie algebra. Highly nontrivial reductions of the given multidimensional problem to those for ODEs are found. New exact solutions are constructed and their properties are established.
S1007570419303016
This paper establishes conditions for the asymptotic stability of timefractional reactiondiffusion systems . The stability of linear systems is investigated by means of the eigenfunction expansion of the Laplacian operator . Theoretical bounds are placed on the arguments of the infinity of eigenvalues belonging to the instant Jacobian matrix . Nonlinear systems are linearized by means of their Taylor series expansion . Numerical solutions of two realistic examples are presented to illustrate the theoretical findings .
This paper considers the local asymptotic stability of time fractional reaction diffusion systems which have been shown to provide accurate models of a variety of natural phenomena. Conditions for the stability of commensurate linear systems are derived by means of the eigenfunction expansion of the Laplacian operator. We show how incommensurate systems can be transformed into commensurate ones. We show how nonlinear systems can be linearized by means of their first order Taylor series approximation.
S1007570419303028
In this work we propose an efficient method to calculate the Hilbert transform of cubic splines . We start by developing an analytical derivation for the problem . Using the structure of the obtained formula we suggest an efficient algorithm to evaluate it . Our method rewrites the cubic spline and reorders calculations to increase the temporal locality of related tasks . Then it creates lookup tables to reuse calculations instead of repeating them . Results show that this method accurately calculates Hilbert transform when applied to functions with a known analytical Hilbert transform . We also show that it significantly reduces the execution time compared to the direct substitution . Our suggested algorithm can be used for the HilbertHuang Transform whose calculation is based on cubic splines and Hilbert transform .
An efficient method to calculate the Hilbert transform of cubic splines by suggesting an efficient algorithm to evaluate it. Our method rewrites the cubic spline and reorders calculations to increase the temporal locality of related tasks. The method reduces the execution time significantly compared to the direct substitution. The method is applicable for HilbertHuang Transform whose calculation is based on cubic splines and Hilbert transform.
S100757041930303X
A broadband piezoelectric energy harvester with a mechanically tunable potential function is modeled and analytically analyzed . The harvester consisting of a beam and a pre compression spring at one end can be tuned to both monostable and bistable configurations . The axial motion of the beam resulting from the transverse vibration and spring load induces two coupled higher order terms of displacement velocity and acceleration into the governing equations . This significantly complicates the theoretical analysis especially the stability analysis of solutions . Harmonic balance method is employed to investigate the dynamic characteristics of the nonlinear energy harvester . An effective approach is developed to solve the entries of the Jacobian matrix for determining the stability of analytical solutions . This approach offers a criterion for solution stability analysis of congeneric nonlinear systems with coupled higher order terms . The energy harvesting performance and the nonlinear dynamic characteristics of the proposed PEH are explored for various base excitation levels electrical resistive loads and pre deformations of the spring . The approximate analytical solutions are validated by numerical simulations . Results demonstrate that the energy harvesting performance of the proposed PEH could be effectively tuned by the pre deformation of the spring . The proposed PEH could harvest vibration energy in a wide frequency range of 091Hz at the excitation level of 0.5g .
A novel nonlinear piezoelectric energy harvester with a tunable potential function is proposed. The harvester is theoretically modeled and the governing equations are derived with coupled higher order terms. The approximate solutions are derived by harmonic balance analysis. An approach is proposed for the stability analysis of the solutions. The harvester has a wide frequency bandwidth over 091Hz at the excitation level of 0.5g.
S1007570419303041
This paper addresses the numerical solution of the multi dimensional variable order fractional integro partial differential equations . The upwind scheme and a piecewise linear interpolation are proposed to approximate the Coimbra variable order fractional derivatives and integral term with kernel respectively . Two new approaches via the Sinc collocation method based on single and double exponential transformations are adopted for the temporal and spatial discretizations respectively . The convergence behaviour of the methods is analysed and the error bounds are provided . In addition four test problems illustrate the validity and effectiveness of the proposed algorithms .
A class of multi dimensional variable order fractional integro partial differential equations is under consideration. New treatments of Sinc spectral method are proposed. The convergence properties of the methods are investigated. The efficiency and accuracy of the proposed methods are analyzed in the perspective of the. norm error and convergence order.
S1007570419303053
The use of a sequence of inter event time intervals as a proxy for time series measurements in state space reconstructions used to compute correlation dimensions is explored . In addition to testing the validity of the method in general the effects of using time intervals that are much longer than the characteristic time scale of the system dynamics are examined . Two model systems for which copious information is available are employed empirically measured data produced using a Chua circuit and computed numerical values produced using a nonlinear model of the reproductive endocrine system . For time intervals well matched to the dynamical time scale the result of state space reconstructions using these time intervals is successful for both the Chua circuit data and the endocrine modeling results . Using longer time intervals however results in computed correlation dimensions that are considerably higher than the actual correlation dimensions of these systems . Similar results are also found using very long delay times in a standard time series analysis of the variables in both systems . Using parameter variations to induce changes in the correlation dimension of the endocrine model system it is shown that these changes are similar in both the actual correlation dimension and the higher correlation dimension computed using very long time intervals . It is argued that this has important implications for studies in which the only available data consists of event intervals as illustrated by comparisons between the endocrine modeling results presented here and empirical studies using menstrual cycle lengths as events intervals .
Event intervals are valid in time series analysis for comparable time scales. Long event intervals can cause correlation dimensions to be too large. Results using long time intervals still reveal valid correlation dimension changes.
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In this paper the bipartite consensus problem is considered for a type of second order multi agent system . Using the signed graph theory the control protocol is designed by means of a distributed impulsive control strategy . Then the problem is transformed into a convergence problem that is presented by the products of a group of general stochastic matrices where the general stochastic matrix means that each row sum is equal to 1 and all entries are not required to be nonnegative . To analyze such a convergence problem some convex hulls are constructed . It is shown that these convex hulls are contractive under the effect of the products of these general stochastic matrices . Subsequently a sufficient criterion is derived to ensure the impulsive bipartite consensus of the system being considered . Finally two numerical examples are given to illustrate the result .
A bipartite consensus problem of second order multi agent systems in which the involved impulsive control protocol does not contain the relative velocity information. A convex analysis approach has been applied to dealing with the considered bipartite consensus problems. Different from the existing works not only this approach can reduce the difficulty of designing control gains but also some constraints in the considered problems can be removed e.g. the velocity of all agents can agree on a certain nonzero value.
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A new analytic multi component gravitational model with three degrees of freedom to describe the orbital properties of stars in a double barred galaxy is introduced . We assume that the galaxy contains two bars the primary one parallel to the disc and the secondary one which is perpendicular to the primary bar . By following the trajectories belonging to large sets of starting conditions we manage to distinguish between localized and escaping motion of stars . The character of orbits is revealed by presenting modern colour coded diagrams on several choices of planes of two dimensions . Additionally we investigate the properties of the normally hyperbolic invariant manifolds associated with the index 1 saddle points of the system . The dynamics near the index 1 saddle points is demonstrated by presenting the bifurcation diagrams of the Lyapunov periodic orbits and by visualizing the restriction of the Poincar maps to the NHIMs . Useful conclusions are drawn by comparing our results with previous related ones from other types of Hamiltonian systems .
We introduce a new analytical gravitational model for describing the motion of stars in double barred galaxies. We reveal the escape dynamics of the system by presenting the corresponding basins of escape of the system. The role of the normally hyperbolic invariant manifolds NHIMs associated with the Lyapunov orbits is investigated.
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The Daisyworld model was originally introduced by Watson and Lovelock in 1983 in order to describe the mechanism of climate homeostasis . Their model which is of zero dimensional one was then extended to a one dimensional model by Adams Carr Lenton and White . They showed that the interactions between white and black daisies and climate give rise to segregation patterns of daisies and suggested existence of some potential link between the homeostatic feedback mechanism and the characters of spatial patterns . In this paper we want to investigate further how such interactions create these segregation patterns and what kinds of patterns are formed by using a two dimensional model . Our results seem to back up Adams Carr Lenton and Whites insight significantly .
Spot island and labyrinth pattern are observed in 2 dimensional Daisyworld model. Characters of patterns are closely related with dimension of the attractor. Turing like mechanisms are on the pattern formation. Some potential link between the homeostatic feedback and spatial patterns exist.
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In the calculation of the map of periods of the Mandelbrot Set and working with fixed point and floating point real number representation systems moire interference patterns always appear . These result from the discretization that every computer sets in the finite encoding of its real values . It is not known from which original layers such interferences are obtained and how these initial layers are generated . This article aims at answering these two questions . In order to search these original layers thousands of images created by means of two different encodings of the real values and with different accuracies of the map of periods were analyzed . Some points with constant location called Source Points around which regular patterns with hyperbolic configuration are generated were located as well . This answers the questions regarding the cause and origin of moire interferences . Some characteristics of Source Points are described hereinafter . It is also justified why moire interferences in the plane of periods have a hypersensitive behavior . Finally it is shown how in dynamic systems accuracy does not only affect the precision of results but also the configuration of the results themselves . The following interesting reflection is therefore open to discussion if the real world should be seen with a fractal way of looking accuracy configurates then the essence of everything .
Moire interference patterns appear in the map of periods of the M Set. These patterns are caused by superimposing hyperbolic structures. These structures are generated around Source Points. Accuracy in dynamic systems configurates the essence of everything. What happens to the discrete magnitudes of the real world
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Explicit formulas for complexity and unique invariant measure of the period doubling subshift can be derived from those for the Thue Morse subshift obtained by Brlek De Luca and Varricchio and Dekking . In this note we give direct proofs based on combinatorial properties of the period doubling sequence . We also derive explicit formulas for correlation integral and two basic characteristics of recurrence quantification analysis of the period doubling subshift recurrence rate and determinism . As a corollary we obtain that RQA determinism of this subshift converges to 1 as the threshold distance approaches0 .
Direct proofs of formulas for complexity and unique invariant measure of the period doubling sequence based on its combinatorial properties are given. Explicit formulas for correlation integrals are derived together with two of the basic measures of recurrence quantification analysis recurrence rate and determinism. The determinism of the period doubling subshift converges to 1 as the threshold distance approaches 0.
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In globally coupled phase oscillators the natural frequency distribution plays a critical role on the synchronization . In this work we consider globally coupled phase oscillators with a multi peak natural frequency distribution that is a superposition of two symmetrical bimodal Lorentzian distributions . Using Ott Antonsen dimension reduction technique we reduce the system from high dimension to low dimension and investigate its dynamical behaviors in detail . Rich dynamical phenomena including revived incoherent states are found . Different types of partial synchronous states are characterized . We further investigate the phenomenon of revived incoherent states in a different view by modifying the model to a system composed of two interacting subpopulations of phase oscillators .
In the investigation of the synchronization in globally coupled phase oscillators with a multi peak natural frequency distribution rich dynamical phenomena including revived incoherent states could be found. By using Ott Antonsen dimension reduction technique the high dimensional coupled phase oscillators can be reduced to two interacting subpopulations of OA oscillators. The stability of the incoherent state and the different types of partial synchronous states can be characterized by using the description of OA oscillators.
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A model of nonlinear elastic medium with internal structure is considered . The medium is assumed to contain cavities microcracks or blotches of substances that differ sharply in physical properties from the base material . To describe the wave processes in such a medium the averaged values of physical fields are used . This leads to nonlinear evolutionary PDEs differing from the classical balance equations . The system under consideration possesses a family of invariant soliton like solutions . These solutions are shown to be spectrally stable under certain restrictions on the parameters .
The conditions for existence of soliton like traveling wave solutions to a non local hydrodynamic model are stated. As a stability test conditions providing the minimum of Hamiltonian subject to the constant momentum with respect to a uniform stretching of systems component is considered. The studies of spectral stability of soliton like solutions incorporating the consideration of the operator of linearization about the traveling wave estimations of the maximal number of unstable modes and stating the conditions for their absence are presented.
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We consider several charged spacecraft configurations around a leader spacecraft provided with an artificial magnetic field . In all configurations the nominal orbits are chosen to be about the relative equilibrium points of the reference model . Using a linear quadratic regulator controller we find that controllability is possible in most of the cases and it is strongly related to the stability of the equilibrium point which in turn depends on the orbit of the leader and the rotation rate of its magnetic dipole .
Formation flight of charged spacecrafts around a spacecraft with a magnetic field. Establishment of configurations around the relative equilibrium points. Formation keeping achieved by merely adjusting the charge on the deputy.
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In this paper we study a 2 parameter family of 2 periodic nonautonomous systems generated by the alternate iteration of two stunted tent maps . Using symbolic dynamics renormalization and star product in the nonautonomous setting we compute the convergence rates of sequences of parameters obtained through consecutive star products renormalizations extending in this way Feigenbaums convergence rates . We also define sequences in the parameter space corresponding to anharmonic period doubling bifurcations and compute their convergence rates . In both cases we show that the convergence rates are independent of the initial point concluding that the nonautonomous setting has universal properties of the type found by Feigenbaum in families of autonomous systems .
We use symbolic dynamics to study a family of periodic nonautonomous tent systems. Sequences of parameters corresponding to consecutive renormalizations are convergent. These convergence rates only depend on the type of renormalization. We obtain new period doubling sequences corresponding to non renormalizable systems. The previous sequences of parameters converge with rate of order 2.
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Phase response curves have been extensively used to control the phase of oscillators under perturbations . Their main advantage is the reduction of the whole model dynamics to a single variable dynamics . However in some adverse situations the phase reduction does not provide enough information and therefore PRC lose predictive power . To overcome this shortcoming in the last decade new contributions have appeared that allow to reduce the system dynamics to the phase plus some transversal variable that controls the deviations from the asymptotic behaviour . We call this setting
We construct a 2D entrainment map based on phase amplitude response functions and study the effect of pulsed periodic inputs. We describe the dynamics on the invariant curves of the 2D map detecting both their breakdown and inner bifurcation cascades. We show that the 2D entrainment map tracks the phase locking dynamics much better than the 1D map standard phase reduction . We show differences in the boundaries of the Arnold tongues between the 2D entrainment map and the 1D map. Our 2D framework can be adapted to many neuronal models and provide realistic paradigms where the 1D phase reduction fails.
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The paper aims at the application of a modified version of the Adomian Decomposition Method to nonlinear bending of laminated thick plates . The Mindlin plate theory along with the equivalent single layer concept is used in this study . The nonlinearity is taken into account through the von Krmn equations . The governing equations of the problem are decomposed into linear and nonlinear terms while the solution is expanded in series as a requirement for constructing the ADM recursive system . The first approximation corresponds to the linear response of the problem . The subsequent ones are incorporations of the problems nonlinearity obtained with the aid of the Adomians polynomials generalised Taylor series around the linear solution particularly tailored for the specific nonlinearity .
A new approach to solve nonlinear bending in laminate thick plates. Incremental approach on the Adomian decomposition method for multivariable problem. Linear solution enhancement to obtain nonlinear solutions. Nonlinear system of equations solved without perturbations or linearisation. Linear term updating to achieve global convergence.
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This article is concerned with the effects of time varying impulses on exponential stability to a unique equilibrium point of inertial Bidirectional Associative Memories neural network with mixed time varying delays . A suitable variable transformation is chosen to transform the original system into a system of first order differential equations . The concept of homeomorphism has been implemented to find a distributed delay dependent sufficient condition which assures that the system has a unique equilibrium point . In order to study the impulsive effects on stability problems a time varying impulses including stabilizing and destabilizing impulses are considered with the transformed system . Based on the matrix measure approach and an extended impulsive differential inequality for a time varying delayed system we have derived sufficient criteria in matrix measure form which ensure the exponential stability of the system towards an equilibrium point for two classes of activation functions . Further different convergence rates of the systems trajectory have been discussed for the cases of time varying stabilizing and destabilizing impulses using the concept of an average impulsive interval . Finally the efficiency of the theoretical results has been illustrated by providing two numerical examples .
Using the concept of homeomorphism a sufficient criterion for ensuring a unique equilibrium point has been derived for the inertial BAM neural networks with mixed time varying delays. The novel concept of average impulsive interval has been applied to remove the requirement of upper or lower bounds of impulsive interval. Based on matrix measure approach and an extended impulsive inequality the exponential stability criteria including averaging impulsive interval have been derived for two classes of activation functions. The convergence rates of the system s trajectories are discussed in detail for different impulsive strengths and distinct classes of activation functions. All theoretical results of this article are numerically verified by giving two examples.
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In this paper the pinning control of fractional complex networks with impulses and time varying delays is studied and a class of more general network structure is considered which consists of an instantaneous communication topology and a delayed communication topology . Based on the linear matrix inequality technique some sufficient conditions are obtained to ensure synchronization of the network under a designed pinning event triggered strategy . And Zeno behaviors are excluded . In addition a pinning scheme is designed which shows that the nodes with delayed communication are good candidates for applying pinning controllers . Finally a numerical simulation is given to verify the correctness of the main results .
A class of fractional complex networks with impulsive effects and time varying delays is introduced and investigated. A class of more general network structure is considered in which all nodes are divided into three categories the nodes which can only send information to others instantly the nodes which can only communicate with others with time delays and the nodes which can not only instantly communicate but also delayed communicate with others. A pinning and event triggered control strategy is proposed to force the network to be synchronized and Zeno behaviors are avoided. By using the theories on algebraic graph a pinning scheme is designed in which some delay coupled nodes should be pinned first.
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In this paper we study strongly RuelleTakens chaos strongly AuslanderYorke chaos and Poincar chaos on the product of semiflows . It is proved that if the finite product or the countably infinite product of semiflows is chaotic then at least one of the factors is chaotic . We also provide necessary examples counterexamples wherever possible related to our results .
Strongly RuelleTakens chaos strongly AuslanderYorke chaos and Poincare chaos are studied on the product of semiflows. It is proved that if the finite or the countably infinite product of semiflows is strongly RuelleTakens chaotic resp. strongly AuslanderYorke chaotic and Poincare chaotic then at least one of the factors is so. Examples counterexamples are also provided related to our results.
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In this paper a Linear Matrix Inequality based approach for designing a robust state feedback controller for a 1 DoF periodically forced impact mechanical oscillator subject to double side rigid barriers constraints and under bounded parametric uncertainties to track another impact oscillator as a master or reference system is proposed . The dynamics of such impact oscillator is defined by a hybrid non autonomous system with impulsive effects for which the impulsive event occurs when the system state encounters the two barriers and the oscillation motion is limited between them . The main idea in the synthesis of the stability conditions lies in the use of the S procedure Lemma and the Finsler Lemma in order to only consider the regions inside which the master slave tracking error evolves . We show that the stability conditions of the tracking error are reformulated by a set of Bilinear Matrix Inequalities . Via the Schur complement Lemma and the Matrix Inversion Lemma a linearization procedure is realized to transform these BMIs into LMIs where the admissible maximum bounds of the parametric uncertainties are maximized . The effectiveness of the proposed feedback controller towards uncertainties is illustrated through simulation results .
A robust feedback control of a 1 DoF impact mechanical oscillator subject to double side rigid constraints and under bounded parametric uncertainty is considered. The control is achieved such that the impact mechanical oscillator as a slave tracks a master impact oscillator adopted as a reference model. The dynamics of the master slave tracking error is described by a non autonomous system with impulsive effects. We use the S procedure Lemma and the Finsler Lemma to only consider the regions within which the system state evolves and hence to develop BMI stability conditions. We use the Schur complement Lemma and the Matrix Inversion Lemma to transform these BMIs into LMIs. A portfolio of numerical simulations is presented to illustrate the master slave tracking.
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This paper studies a class of quasi linear impulsive systems of functional differential equations with infinite time delay . By employing the contraction principle several criteria on uniform stability and asymptotic stability are established . The proposed approach utilizes the idea of averaging instead of the point wise estimate in the Lyapunov method . Our results show that the Banach contraction principle can be used as a possible alternative to Lyapunov methods for stability analysis when the conditions of Lyapunov method fails to hold . Several examples are discussed to illustrate the ideas of our results .
This paper studies a class of quasi linear impulsive systems of functional differential equations with infinite time delay. It uses the Banach contraction principle. It has established criteria on uniform stability and asymptotic stability. The proposed approach utilizes the idea of averaging instead of the point wise estimate in the Lyapunov method. It shows that the Banach contraction principle can be used as a possible alternative to Lyapunov methods for stability analysis when the conditions of Lyapunov method fails to hold.
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This paper analyses some operators recently proposed either as alternatives or as generalizations of classical fractional derivatives . The performance assessment both under the point of view of system theory and signal processing demonstrates that two approaches do not follow some systematic criteria . Therefore this paper contributes towards a systematic and careful study of the new proposals in the scope of the fast evolving area of Fractional Calculus .
Definition of suitable criterion for fractional derivatives. Analysis of some operators under the light of fractional calculus. Relevance of the index law.
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Due to the requirement of signal representations flexibility for strong noise interference in non stationary signal processing the traditional ChoiWilliams distribution is extended to the linear canonical domain by using a well established closed form instantaneous cross correlation function type of linear canonical transform free parameters embedded approach . The derived CICF type of CWD unifies all of the linear canonical ChoiWilliams distributions and can be considered as the CWDs closed form representation in linear canonical domains . The CICFCWD of a discrete time signal defined by the sampling equation is discussed for the requirement of digital signal analysis and processing . To break through the limitation that the existing research techniques are limited to quantitative analysis based on numerical simulations a qualitative analysis to output signal to noise ratio inequality between the traditional CWD and the CICFCWD for a general noisy signal is introduced including the inequality modeling and solving . Within this output SNR improvement analysis framework the strategies on determination LCT free parameters for linear frequency modulated signals added with white noise are developed . Numerical experiments are also carried out to validate the correctness of LCT free parameters selection results and the feasibility of output SNR improvement analysis approach .
Introduce linear canonical transform free parameters into ChoiWilliams distribution. Output SNR improvements mathematical model an output SNR inequality. LCT free parameters selection results on LFM signals added with white noise.
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Coupled dispersionless equation is an important model in quantum physics . Complex coupled dispersionless equation has valuable applications in geomerty . Recently Ablowitz and Musslimani introduced and investigated a large class of reverse space reverse time and reverse space time nonlocal integrable equations . In this paper we investigate a reverse space time nonlocal complex coupled dispersionless equation which was proposed in our paper . By means of the Darboux transformation we obtain its multi soliton solutions from zero seed and nonzero seed . The asymptotic behavior of these solutions is discussed .
Multi soliton solutions for a reverse space time nonlocal complex coupled dispersionless equation are constructed. The asymptotic behavior of these multi soliton solutions is discussed. Darboux transformation of the reverse space time nonlocal complex coupled dispersionless equation is given.
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In this paper signal propagation is analysed in electromagnetic media described by fractional order models . Maxwells equations with FO constitutive relations are introduced in the time domain . Then their phasor representation is derived for one dimensional case of the plane wave propagation . With the use of the Fourier transformation the algorithm for simulation of the non monochromatic wave propagation is introduced . Its implementation in Matlab allows for generation of time domain waveforms of signals propagating in the media described by FOMs . It is demonstrated that despite high attenuation a small perturbation of the time derivative orders in Maxwells equations allows for tuning of the time of signal arrival to the observation point . In all the cases studied the rate of pulse advancement increases with simultaneous decrease of the value of the time derivative orders in FO Maxwells equations .
In this paper the signal propagation is analysed in electromagnetic media described by fractional order FO models FOMs . Maxwells equations with FO constitutive relations are introduced in the time domain. With the use of the Fourier transformation the algorithm for simulation of the non monochromatic wave propagation is introduced. Its implementation in software allows for generation of time domain waveforms of signals propagating in media described by FOMs. It is demonstrated that despite high attenuation a small perturbation of the time derivative orders in Maxwells equations allows one to advance the time of signal arrival to the observation point. In all the cases studied the rate of pulse advancement increases with simultaneous decrease of the value of the time derivative orders in FO Maxwells equations.
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In this paper an interval observer is synthesized for fractional linear systems with additive noise and disturbances . The contribution of system whole past to future output is taken into account as an initialization function . Provided the initialization function is upper and lower bounded it is shown in this paper that the fractional interval observer allows to bound pseudo state free responses by an upper and a lower trajectory . In case interval observers can not be synthesized straightforwardly so as to obtain a stable and non negative estimation error it is shown that a change of coordinates allows to overcome this problem . The proposed methodology allows to bound fractional systems trajectories when the whole past is unknown but can be bounded . Finally a numerical example is given to show the effectiveness of the proposed methods on the initialization of fractional linear systems .
An interval observer is synthesized for fractional linear systems with additive noise and disturbance. Fractional interval observer is used to bound pseudo state free response by an upper and a lower trajectory which is useful when system initial conditions are unknown. A static linear transformation of coordinates is proposed when interval observer cannot be synthesized straightforwardly.
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The first order term in the geometric optics approximation to the solution of an hyperbolic differential system is known to satisfy a transport equation along rays which is analogous to the Burgers equation . As such it usually develops shocks . The second order term satisfies a linear transport equation whose coefficients depend on the first order solution these coefficients are detailed for the case of fast magnetosonic waves in a simple equilibrium state . The problem is that the solutions to this second order equation will blow up as soon as the first order term develops a shock . This fact is analyzed and its relevance to the validity of the asymptotic approximation discussed .
The second order term in the geometric optics approximation is studied for magnetosonic waves. The transport equation is detailed. The equation is integrated along characteristics. The second order term undergoes a blow up the moment the first order one becomes a shock wave.
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Escape from a potential well can occur in different physical systems such as capsize of ships resonance transitions in celestial mechanics and dynamic snap through of arches and shells as well as molecular reconfigurations in chemical reactions . The criteria and routes of escape in one degree of freedom systems have been well studied theoretically with reasonable agreement with experiment . The trajectory can only transit from the hilltop of the one dimensional potential energy surface . The situation becomes more complicated when the system has higher degrees of freedom since the system state has multiple routes to escape through an equilibrium of saddle type specifically an index 1 saddle . This paper summarizes the geometry of escape across a saddle in some widely known physical systems with two degrees of freedom and establishes the criteria of escape providing both a methodology and results under the conceptual framework known as tube dynamics . These problems are classified into two categories based on whether the saddle projection and focus projection in the symplectic eigenspace are coupled or uncoupled when damping and or gyroscopic effects are considered . For simplicity only the linearized system around the saddle points is analyzed but the results generalize to the nonlinear system . We define a transition region
For the first time both dissipative and gyroscopic forces are considered in the context of the geometric theory of tube dynamics for escape across an index 1 saddle. In. degrees of freedom the boundary of transit orbits starting at the same initial energy goes from a 2. 2 dimensional hyper cylinder in the conservative case to a 2. 2 dimensional hyper ellipsoid in the dissipative case. Several two degree of freedom example systems are considered that illustrate escape from potential wells and they are classified into systems with coupled or uncoupled saddle focus dynamics. A gyroscopic system with any amount of damping and an inertial system with unequal damping in the multiple degree of freedom case both have coupled dynamics of the saddle and focus projections in the symplectic eigenspace.
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In this manuscript an approximate technique is established to determine the stationary response probability density of nonlinear stochastic systems . The stationary probability density is assumed to be an exponential function with the power constituted by two specified parts the first part is the power of the analytical solution of the associated degenerated system while the second is an additional polynomial function of state variables with to be determined coefficients . Substituting the exponential form expression into Fokker Planck Kolmogorov equation yields the residual error and the coefficients can be determined by minimizing the mean square value of this residual error . Furthermore the accuracy of the proposed method can be improved by an iterative procedure . Several typical examples including van der Pol Duffing system Column frictional system and a nonlinear system with complex damping and stiffness are systematically investigated to demonstrate the validity and efficiency of the proposed method .
The stationary probability density is an exponential function with power constituted by two specified parts. The first part is the power of analytical solution of a degenerated system. The second part is a state dependent polynomial with to be determined coefficient. The proposed method can be applied to system with high dimension and strongly nonlinear.
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This paper investigates fault tolerant secure consensus tracking for delayed nonlinear multi agent systems with deception attacks uncertain parameters and actuator failure via impulsive control . The deception attacks are considered in the information exchange channels among neighbour agents and it would be modeled as a Bernoulli distribution . A class of distributed impulsive control protocols is proposed . Some sufficient conditions for achieving mean square bounded consensus are obtained . The mean square error bounds are derived which are associated with the energy of deception attack and the expectation matrix involved with actuator failure . Simulations are provided to illustrate the effectiveness of the proposed control scheme .
Fault tolerant secure consensus tracking of nonlinear multi agent systems with deception attacks via impulsive control is considered. The actuator failure parameters fluctuation and time delay are simultaneously taken into consideration. A class of distributed impulsive control protocols is proposed for a secure consensus tracking problem to reduce the influence of fault data on the stability of the system. The mean square error bounds are derived.
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We investigate the effects of spin orbit coupling and Zeeman splitting on the coupled density spin dynamics and collapse of the BoseEinstein condensate driven by the quintic self attraction in the same and cross spin channels . The characteristic feature of the collapse is the decrease in the width as given by the participation ratio of the density rather than by the expectation values of the coordinate . Qualitative arguments and numerical simulations reveal the existence of a critical spin orbit coupling strength which either prohibits or leads to the collapse and its dependence on other parameters such as the condensates norm spin dependent nonlinear coupling and the Zeeman splitting . The entire nonlinear dynamics critically depends on the initial spin sate .
The collapse of BEC is characterized by the participation ratio of density. Effects of the SOC and ZS depend on the form of the quintic nonlinearity. 1D collapse is controlled by the interplay of self attraction and splitting. The initial spin state critically influences the collapse dynamics.
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In this paper dynamics of higher order localized waves for a coupled nonlinear Schrdinger equation are investigated . Based on the generalized Darboux transformation the first to the third order interactional localized wave solutions are derived through algebraic iteration . Specially the new form of seed solutions is supposed which is related to the normalized distance and retarded time . Many novel dynamic structures are demonstrated in the localized waves particularly the third order localized ones where rogue waves coexist with dark bright solitons and breathers in the three dimensional plots . Furthermore the classification of the
Higher order localized wave solutions are studied for a coupled nonlinear Schrdinger equation. A new form of seed solutions is supposed. Dynamics of localized waves are discussed especially the third order ones which are not studied in the previous paper. Display some interesting and novel plots.
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We investigate the structure and the nonlinear dynamics of two rigid polar rotors coupled through the dipole dipole interaction in an external homogeneous electric field . In the field free stable head tail configuration an excess energy is provided to one of the dipoles and we explore the resulting complete dimensional classical dynamics . This dynamics is characterized in terms of the kinetic energy transfer between the dipoles their orientation along the electric field as well as their chaotic behavior . The field free energy transfer mechanism shows an abrupt transition between equipartition and non equipartition regimes which is independent of the initial direction of rotation due to the existence of an infinite set of equivalent manifolds . The field dressed dynamics is highly complex and strongly depends on the electric field strength and on the initial conditions . In the strong field regime the energy equipartition and chaotic behavior dominate the dynamics .
Theoretically investigation of two interacting classical rigid dipoles in the presence of a homogenous electric field. The classical dynamics of the two dipoles is explored in terms of the energy transfer mechanisms between them and their orientations along the electric field axis. In the field free case the system falls to either an energy equipartition regime or a non equipartition one and the dynamics is regular. In the presence of the field the classical dynamics strongly depend on the electric field strength and on the initial conditions. For weak external fields the dynamics is dominated by the dipole dipole interaction and the energy transfer dynamics resembles the field free dynamics. By increasing the electric field the interaction with this field dominates the classical dynamics and the orientation of the two dipoles along the electric field direction increases. Even for large electric field strengths the system shows a highly chaotic behavior.
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In this work we study the stability properties of the ground states of a spin 1 Bose gas in presence of a trapping potential in one spatial dimension . To set the stage we first map out the phase diagram for the trapped system by making use of a so called continuous time Nesterov method . We present an extension of the method which has been previously applied to one component systems to our multi component system . We show that it is a powerful and robust tool for finding the ground states of a physical system without the need of an accurate initial guess . We subsequently solve numerically the Bogoliubov de Gennes equations in order to analyze the stability of the ground states of the trapped spin 1 system . We find that the trapping potential retains the overall structure of the stability diagram while affecting the spectral details of each of the possible ground state waveforms . It is also found that the peak density of the trapped system is the characteristic quantity describing dynamical instabilities in the system . Therefore replacing the homogeneous density with the peak density of the trapped system leads to good agreement of the homogeneous Bogoliubov predictions with the numerically observed maximal growth rates of dynamically unstable modes . The stability conclusions in the one dimensional trapped system are independent of the spin coupling strength and the normalized trap strength over several orders of magnitude of their variation .
Stability properties by numerically solving the Bogoliubov de Gennes equations. The trapping potential retains the overall structure of the stability diagram. Stability conclusions independent of spin coupling and normalized trap strength. Mapping out the phase diagram by making use of a continuous time Nesterov method.
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The long term dynamics of perturbed Keplerian motion is usually analyzed in simplified models as part of the preliminary design of artificial satellites missions . It is commonly approached by averaging procedures that deal with literal expressions in expanded form . However there are cases in which the correct description of the dynamics may require full contrary to simplified potential models as is for instance the case of low altitude high inclination lunar orbits . In these cases dealing with literal expressions is yet possible with the help of modern symbolic algebra systems for which memory handling is no longer an issue . Still the efficient evaluation of the averaged expressions related to a high fidelity potential is often jeopardized for the expanded character of the output of the automatic algebraic process which unavoidably provides huge expressions that commonly comprise tens of thousands of literal terms . Rearrangement of the output to generate an efficient numerical code may solve the problem but automatization of this kind of post processing is a non trivial task due to the ad hoc heuristic simplification procedures involved in the optimization process . However in those cases in which the coupling of different perturbations is not of relevance for the analysis the averaging procedure may preserve the main features of the structure of the potential model thus avoiding the need of the typical blind computer based brut force perturbation approach . Indeed we show how standard recursions in the literature may be used to efficiently replace the brut force approach in this way avoiding the need of further simplification to improve performance evaluation . In particular Kaulas seminal recursion formulas for the gravity potential reveal clearly superior to the use of both expanded expressions and other recursions more recently proposed in the literature . Thus after making a general assessment on the computational efficiency of the different approaches to compute the zonal gravitational potential in mean elements the need of using high degrees of the gravitational potential for mission design purposes is illustrated for the case of a low lunar orbit .
Kaula s recurrences for long term geopotential motion are discussed. They show better performance over other recursions in the literature. They are useful in exploring analytically the long term dynamics. They help in disclosing the required complexity of the dynamical model.
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Solitons breathers and rogue waves of the coupled Hirota system are investigated . To obtain these solutions we construct the 44 Lax pair and Darboux transformation . With zero backgrounds we derive the one and two peak solitons . With non zero and mixed backgrounds we produce a family of the breather solutions and rational solutions for the purpose of describing the rogue waves . The second order rogue wave solutions on the mixed backgrounds are obtained . The existence and properties of bright dark breathers and rogue waves are discussed . By adjusting the parameters in DT we show the conversions between the bright breathers rogue waves and the dark breathers rogue waves in the course of evolution . We note that for such system if there is the modulation instability it is of baseband type only .
Soliton breather and rogue wave solutions are obtained via Darboux transformation. Modulation instability of the coupled Hirota system is discussed. Dynamics of bright dark rogue waves breathers are investigated.
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The numerical discretization of the ZakharovShabat Scattering problem using integrators based on the implicit Euler method trapezoidal rule and the split Magnus method yield discrete systems that qualify as AblowitzLadik systems . These discrete systems are important on account of their layer peeling property which facilitates the differential approach of inverse scattering . In this paper we study the Darboux transformation at the discrete level by following a recipe that closely resembles the Darboux transformation in the continuous case . The viability of this transformation for the computation of multisoliton potentials is investigated and it is found that irrespective of the order of convergence of the underlying discrete framework the numerical scheme thus obtained is of first order with respect to the step size .
This paper draws a connection between discrete systems proposed for the ZakharovShabat scattering problem and the AblowitzLadik problems. A simple intuitive derivation of the discrete Darboux transformation is provided for each of the discrete systems considered. The order of convergence of each of the methods is estimated and numerically verified.
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We analyze the intermittent regime which develops in an air conveying soft tube . The very thin walls of the tube allow the pipe to fluctuate with high amplitudes and to exhibit kinks in its shape . As a consequence the flow pressure alternates between turbulent and laminar phases . In the experiment the turbulent phase durations scale exponentially while the laminar phases display algebraic statistics . The coexistence of these two distinct laws for the same value of the control parameter value can be modeled on the basis of two competing stochastic processes with different time scales . The first one refers in our case to the local flow velocity and the other one is a critical velocity related to the tube geometrical variable shape which is quenched during the laminar phases but rapidly varying during the turbulent phases . The model reveals that the modification of the ratio
Sky Dancers display intermittent behavior with several metastable configurations. Turbulent and laminar regimes show very different statistical behaviors. The competition of two time scales in the system may shed light on this phenomenon.
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We perform a numerical study of the initial boundary value problem with vanishing boundary conditions of a driven nonlinear Schrdinger equation with linear damping and a Gaussian driver . We identify Peregrine like rogue waveforms excited by two different types of vanishing initial data decaying at an algebraic or exponential rate . The observed extreme events emerge on top of a decaying support . Depending on the spatial temporal scales of the driver the transient dynamics prior to the eventual decay of the solutions may resemble the one in the semiclassical limit of the integrable NLS or may e.g . lead to large amplitude breather like patterns . The effects of the damping strength and driving amplitude in suppressing or enhancing respectively the relevant features as well as of the phase of the driver in the formation of a diverse array of spatiotemporal patterns are numerically analyzed .
Emergence of rogue waves for the linearly damped and localized driven NLS. Semi classical type dynamics and breather patterns depending on the spatiotemporal scales of the Gaussian driver. The impact of forcing amplitude damping strength and rate of decay of the initial data on various characteristics or rogue waves. The impact of the phase of the driver on spatiotemporal pattern formation.
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In this paper we present pinning boundary conditions for two and three dimensional phase field models . For the 2D and axisymmetric domains in the neighborhood of the pinning boundaries we apply an odd function type treatment and use a local gradient of the phase field for points away from the pinning boundaries . For the 3D domain we propose a simple treatment that fixes the values on the ghost grid points beyond the discrete computational domain . As examples of the phase field models we consider the AllenCahn and conservative AllenCahn equations with the pinning boundary conditions . We present various numerical experiments to demonstrate the performance of the proposed pinning boundary treatment . The computational results confirm the efficiency of the proposed method .
Efficient and simple pinning boundary conditions are proposed. Accurate interpolation schemes for the boundary points are used. The efficient and accuracy of the proposed method were tested.
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Recurrence plot is a visual tool to study complex time series . Its construction involves the threshold selection . Recurrence quantification analysis aims at describing the complexity and structural characteristics of RP . Different thresholds produce different quantitative analysis results . In this paper an adaptive threshold selection technique based on cumulative histogram method is proposed . In order to overcome the large computational complexity of CHM we introduce a symbolic representation of time series symbolic aggregate approximation . Through experiments on simulated data and comparing the results of the original threshold selection our modified method shows a certain application prospect . Some interesting results are found when we apply it to the financial stock markets .
An adaptive method for threshold of recurrence quantification analysis is proposed. Symbolic Aggregate approximation can reduce the computational complexity of the method. Our method is robust to sequence length noise and sampling frequency. Some interesting results are obtained when applied to financial time series.
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The brain can be considered as a system that dynamically optimizes the structure of anatomical connections based on the efficiency requirements of functional connectivity . To illustrate the power of this principle in organizing the complexity of brain architecture we portray the functional connectivity as diffusion on the current network structure . The diffusion drives adaptive rewiring resulting in changes to the network to enhance its efficiency . This dynamic evolution of the network structure generates and thus explains modular small worlds with rich club effects features commonly observed in neural anatomy . Taking wiring length and propagating waves into account leads to the morphogenesis of more specific neural structures that are stalwarts of the detailed brain functional anatomy such as parallelism divergence convergence super rings and super chains . By showing how such structures emerge largely independently of their specific biological realization we offer a new conjecture on how natural and artificial brain like structures can be physically implemented .
Adaptive rewiring drives the emergence of brain like network structures. Global properties of structural evolution now match local ones. The proposed model explains the emergence of super chains rings and ganglions. Superstructures can embed synfire chains and polychronous sets.
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Multistability is a common feature of various dynamical systems which manifests itself as the possibility to demonstrate various behaviors for the same parameter values . These behaviors or states of the system must be stable against weak perturbation in order to be observable in real life . However a strong enough perturbation may destroy a certain state and lead to the system switching to another one . From the viewpoint of nonlinear dynamics the response of a multistable system to a strong stimulus depends on the configuration and the mutual arrangement of basins of different attractors . In the present paper we introduce a novel measure for characterization of a multistable system the switching threshold . It equals the amplitude of a minimal perturbation capable of switching the system from one attractor to another . We develop a numerical algorithm for calculation of the switching thresholds and apply it to a number of paradigmatic models including dynamical networks . We show that the values of switching thresholds provide important information about multistable systems and their responses to external stimuli . This information allows to develop methods of optimal control of multistable systems by external signals . Surprisingly it also allows to predict some features of their dynamics under the influence of external noise .
The switching threshold is a novel quantitative measure to characterize the response of multistable dynamical systems to strong perturbations. A numerical algorithm for quantification of the switching threshold for a wide class of dynamical systems is suggested. The values of switching thresholds allow to predict various features of the stimulus induced dynamics and also to perform optimal control.
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This study provides basic instantaneous source functions for different source reservoir geometries in infinite fractal reservoirs and infinite slab FRs . The concept of fractal geometry has already been adopted to analyse and model well reservoir systems with complex structures . All these complexities have been modelled through a partial differential equation called fractal diffusivity equation . In this paper by use of the source Greens function technique we analytically solve the FDE for different boundary conditions i.e . different source reservoir geometries . The wellbore pressure response for horizontal wells in an infinite slab FR is derived and analysed to illustrate the applications of the provided analytical source solutions and how to use these solutions .
Utilizing the fractal geometry to develop instantaneous source function. Analyzing the infinite reservoir and infinite slab reservoirs using the introduced source functions. Developing novel models for complex real reservoirs with complex structures via different types of mathematical dimensions.
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The high performing nonlinear vibration energy harvesters are conventionally investigated when integrated with simplified resistive electrical circuits while in fact DC voltages are needed for electronics and rechargeable batteries in practical applications . To lead to an accurate and effective set of design guidelines for realistic energy harvesting system development an analytical harmonic balance based method is proposed to characterize the steady state performance and investigate the DC circuit effects . During the route of the analysis method the induced nonlinear piecewise piezovoltage is firstly approximated via smooth dynamic responses based on the energy equivalence which enables the followed harmonic balance operation to analytically estimate the vibration amplitude . The parameter studies show the pros and cons of the coupling constant and resistive load . In one side with increasing the coupling constant or load resistance during their moderate range higher electric power is extracted . In the other side higher piezoelectric coupling and resistive load compromise the beneficial bandwidth of snap through vibrations . Moreover comparisons are conducted to reveal the different structural roles of the standard electrical circuit and AC circuit . It is found that AC circuit exhibits equivalent damping effect while the standard rectifying electrical circuit exhibits both equivalent damping and stiffness effects to the harvester system . These different circuit effects explain the theoretically predicted and numerically validated phenomena that the standard rectifying electrical circuit extracts less electric power than AC circuit under moderate piezoelectric coupling constants and resistive loads while outperforms AC circuit when the coupling constants or load resistances are relatively large .
This research established an analytical method to predict the electrical energy storage performance of harmonically excited nonlinear bistable vibration energy harvester interfaced with a standard rectifying electrical circuit. Numerical and experimental efforts are employed to thoroughly validate the insights derived from the theoretical development. The approach provides an effective tool to identify the influence of harmonic excitation and system design parameters on the dynamic responses and the harvested power as well as to determine the optimal system parameters leading to high extracted power. The roles of the standard rectifying electrical circuit and simplified AC circuit are investigated as well as qualitatively and quantitatively compared.
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This paper studies the controllability of complex valued impulsive systems with time varying delays in control input . The impulsive systems considered here have a complex valued state space for some typical examples such as biological neural networks and quantum systems can be described by such systems . Using the method of variation of parameters an explicit expression of the solution for the given system is established . Based on the solution so obtained several controllability criteria are presented for such systems . Necessary and sufficient conditions for controllability are further derived for the time invariant case . It is shown that controllability of such systems is dependent on the impulsive function in discrete time the system matrices in continuous time and the time delay in control . Three numerical examples are presented to demonstrate the effectiveness of the developed controllability results .
Controllability of impulsive system with time varying delay is investigated in complex valued state space for the first time. Derive several sufficient or necessary conditions for two kinds of controllability. Further concise necessary and sufficient conditions for controllability are obtained when system is reduced to a special case. Different from some known results the derived conditions are less conservative and more general.
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Adaptive management of traffic congestion in the Internet is a complex problem that can gain useful insights from a dynamical approach . In this paper we propose and analyze a one dimensional discrete time nonlinear model for Internet congestion control at the routers . Specifically the states correspond to the average queue sizes of the incoming data packets and the dynamical core consists of a monotone or unimodal mapping with a unique fixed point . This model generalizes a previous one in that additional control parameters are introduced via the data packet drop probability with the objective of enhancing stability . To make the analysis more challenging the original model was shown to exhibit the usual features of low dimensional chaos with respect to several system and control parameters e.g . positive Lyapunov exponents and Feigenbaum like bifurcation diagrams . We concentrate first on the theoretical aspects that may promote the unique stationary state of the system to a global attractor which in our case amounts to global stability . In a second step those theoretical results are translated into stability domains for robust setting of the new control parameters in practical applications . Numerical simulations confirm that the new parameters make it possible to extend the stability domains in comparison with previous results . Therefore the present work may lead to an adaptive congestion control algorithm with a more stable performance than other algorithms currently in use .
Random Early Detection RED is an algorithm for congestion control in the Internet. We propose a generalization of a previous discrete time nonlinear RED model with two additional control parameters and study its global stability. Numerical simulations show that the generalized model is more stable than the original one. We obtain parametric regions for robust settings of the new parameters.
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Grey prediction models have been widely used in various fields and disciplines . Cumulative sum operator also called accumulative generation operator is an essential step in grey modelling but until now relatively limited attention has been paid to its mechanism of action . In this paper we introduce the integral matching to explain it . By using the integral transformation the grey prediction model whose nature is modelling the cumulative sum series with a differential equation proves to be equivalent to that modelling the original series with a reduced differential equation . The cumulative sum operator is the discretization and approximation of the definite integral terms by using the piecewise constant integral and thus can be improved by using the piecewise linear integral . Simulation studies detail the advantages in terms of the stability and robustness to noise .
We investigate the mechanism of cumulative sum operator in grey prediction model by using integral transformation. We provide a novel paradigm for estimating the structural parameters and the initial value simultaneously. We analyze the influence of sample size and noise level on modelling performance by using large scale simulation studies.
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Recently scaled Brownian motion has attracted considerable attention in the context of single particle tracking experiments displaying anomalous fractional dynamics . Its probability density function coincides with the one for fractional Brownian motion . On the other hand scaled Brownian motion displays weak ergodicity breaking . In this paper we show that by applying the so called Lamperti transformation we are able to transform the scaled Brownian motion into ergodic process . This allows us to estimate the distribution and moments of the studied process having only one appropriately long trajectory . We apply the same method to the scaled fractional Brownian motion and stable Lvy motion . It appears that the method works also in the case of long range correlations and heavy tailed distributions . We confirm our theoretical results using numerical simulations .
we show that scaled Brownian motion after Lamperti transformation is ergodic. we demonstrate how to transform a non ergodic anomalous diffusion process in order to recover the ergodicity property. we apply Lamperti transformation to estimate moments and distribution having only one trajectory of the analyzed weakly non ergodic process. we apply the method to some generalizations of scaled Brownian motion in particular we analyze scaled fractional Brownian motion and scaled stable Levy motion. we demonstrate efficiency of our method using simulated data for the studied processes.
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In this paper the reliability analysis of vibro impact system with both randomly fluctuating restoring and damping terms is studied by a modified path integration method . Specifically the Ivanov nonsmooth transformation technique is adopted to transform the vibro impact system into the system without barrier then the modified PI application on vibro impact systems is applied which is based on the Gaussian closure method and the localized approximation of moment function . According to the first passage theory the reliability function the first passage probability density function and the mean first passage time are numerically calculated . In the framework of our numerical results the influences of different random restoring terms random damping terms and impact conditions on the systems reliability are discussed . The modified PI results are compared with the Monte Carlo Simulation results which shows that the proposed PI method can not only provide sufficiently accurate results to observe the weak influence of parameters but also has obvious advantages in computational efficiency .
Reliability analysis of vibro impact system under random excitations is meaningful but seldom reported before and this articles study is about it. The restoring and damping terms may exhibit some degree of random fluctuation in certain types of mechanical structure so this paper discussed the influence of random varying restoring and damping terms on the systems reliability. The influence of impact conditions on the systems reliability is also studied and the numerical results are quite abundant. The research method is a recently proposed path integration PI method which is specially modified and some procedures are quite innovative. The comparison of Monte Carlo simulation MCS shows that the numerical PI results are accurate enough to observe the weak influence of parameters on the reliability. Whats more the PI method has significant advantage in efficiency when dealing with this type of system.
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In this paper a general method to establish the asymptotic behaviour of solutions to multi order multiple time varying delays nonlinear systems is proposed . The method relying on vector Lyapunov like functions and on comparison arguments reduces the asymptotic stability problem to verify a Hurwitz property on a suitable matrix . Many results in integer order systems can be easily generalized to multi order systems since the obtained conditions are order independent . The latter fact is exploited to obtain robust results when the derivation order is uncertain . To establish the method robust multi order multiple time varying delays linear positive systems are studied generalizing previous results existing in the literature . Two illustrative examples are presented the main one providing conditions for asymptotic stability of a multi agent multi order system with time varying delay .
A simple method to establish the asymptotic stability and the robustness of solutions to multi order multiple time varying delays nonlinear systems is proposed. In order to establish the method the asymptotic stability and the robustness properties of multiple order multiple time varying delays positive linear systems are analysed. Two illustrative examples are provided. The first one shows the control of a multi order nonlinear system without delays and the second one posits conditions for asymptotic stability and robustness of a multi agent multi order system with time varying delays.
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In this article a chaos analysis is performed for the viscoelastic nonlinear coupled dynamics of perfectly straight nanotubes conveying pulsatile fluid for the first time . A size dependent advanced elasticity model is developed with consideration of stress nonlocality as well as the gradient of strain components . After presenting the nonlinear motion equations using Hamilton s approach they are numerically solved via application of a time integration technique for a system with a large number of degrees of freedom . Chaos analysis is performed for the nanotube at both subcritical and supercritical flow regimes . Both mean fluid velocity and the amplitude of velocity pulsation are varied as the bifurcation parameter . The proposed size dependent continuum modelling and numerical results would be useful in order to tailor the system parameters to avoid chaos in nanoelectromechanical devices using fluid conveying nanotubes .
The chaotic behaviour of nanotubes conveying pulsatile nanofluid is studied. A scale dependent model considering geometrical nonlinearity is developed. The continuum model contains two distinct scale parameters. Both transverse and axial inertial effects are taken into consideration. The chaotic behaviour is greatly influenced by flow pulsation.
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It is shown how classes of modulated coupled systems of sine Gordon Demoulin and Manakov type may be reduced to their unmodulated counterparts via the application of a novel reciprocal transformation . Modulations governed by recently introduced integrable Ermakov Painlev II Ermakov Painlev III and Ermakov Painlev IV equations as well as the classical Ermakov equation are considered . In the latter case the procedure is illustrated by the generation of a class of exact solutions to a heterogeneous Manakov system with periodic modulation .
Privileged integrable systems admit reciprocally related modulated counterparts. Modulation may be driven by Painlev and Ermakov equations. Periodically modulated Manakov solitons may be obtained.
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In this paper we propose and simulate novel multi fractal multi resolution structures which arise when hybrid schemes formed by Diffusion Limited Aggregation and Strange Attractors are considered . First DLA aggregates formed with a given attachment radio
We describe and simulate multi fractal multi resolution structures. Hybrid Diffusion Limited Aggregation Strange Attractors are proposed. Super Cumulus of multi fractal structures are also simulated.
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The identification of the minimal set of nodes that maximizes the propagation of information is one of the most relevant problems in network science . In this paper we introduce a new method to find the set of initial spreaders to maximize the information propagation in complex networks . We evaluate this method in assortative networks and verify that degree degree correlation plays a fundamental role in the spreading dynamics . Simulation results show that our algorithm is statistically similar regarding the average size of outbreaks to the greedy approach in real world networks . However our method is much less time consuming than the greedy algorithm .
Network assortativity impacts on the results of the influence maximization methods. More spreaders may not provide additional informed nodes at the end of the dynamic. Selecting the best spreaders by communities performs similarly to the Greedy approach. It is more suitable and less time consuming the selection of spreaders by communities.
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Mathematical models based on nonsmooth dynamical systems with delay are widely used to understand complex phenomena specially in biology mechanics and control . Due to the infinite dimensional nature of dynamical systems with delay analytical studies of such models are difficult and can provide in general only limited results in particular when some kind of nonsmooth phenomenon is involved such as impacts switches impulses etc . Consequently numerical approximations are fundamental to gain both a quantitative and qualitative insight into the model dynamics for instance via numerical continuation techniques . Due to the complex analytical framework and numerical challenges related to delayed nonsmooth systems there exists so far no dedicated software package to carry out numerical continuation for such type of models . In the present work we propose an approximation scheme for nonsmooth dynamical systems with delay that allows a numerical bifurcation analysis via continuation methods using existing numerical packages such as COCO . The approximation scheme is based on the well known fact that delay differential equations can be approximated via large systems of ODEs . The effectiveness of the proposed numerical scheme is tested on a case study given by a periodically forced impact oscillator driven by a time delayed feedback controller .
We propose a numerical approach to study nonsmooth DDEs via continuation methods. The approach is based on the approximation of DDEs via large systems of ODEs. Discretization of delay interval and Taylor expansions are used for approximation. The approach is tested on an impact oscillator with time delayed feedback control. The system is analyzed via path following methods implemented in the software COCO.
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This paper investigates the local stability and stabilization problem of nonlinear time delay systems subject to parameter uncertainties which are represented by interval type 2 T S fuzzy systems with two additive time varying delays . Because T S fuzzy models often represent primitive nonlinear systems well only in the region of validity local stability and stabilization problems are considered . By constructing a novel LyapunovKrasovskii functional and using the matrix inequality scaling approach a new delay dependent local stability and stabilization criterion is derived in terms of linear matrix inequalities . Using Lyapunov level set the estimation of attraction domain is also developed . Finally two numerical examples are employed to verify the effectiveness of proposed methods .
The stability analysis and control design for nonlinear systems with two additive delays and parameter uncertainties are investigated via IT2 T S fuzzy model. The local stability analysis and synthesis of IT2 T S fuzzy model with two additive delays are investigated. The problem of estimation of attraction domain is also considered. A novel Lyapunov function is constructed and the General Free Weight Matrix approach is introduced to the derive less conservative local stability and stabilization conditions in the form of LMIs.
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In this study two generalized Duffing systems which are not directly coupled but subjected to a common stochastic excitation are studied to address the problem of chaotic synchronization . Three types of stochastic diffusion processes generated by the first order filter are taken as driving excitations and employed to survey their effects on the onset of synchronization with identical spectral densities but different probability density functions . By applying the mean largest Lyapunov exponent we observe that synchronization can indeed occur in the chaotic Duffing systems when the excitation amplitudes are sufficiently larger than the thresholds needed of the synchronization response . Meanwhile we show the effects for the three diffusion processes on the onset of synchronization are similar . Above all the most noteworthy result of this work is that the synchronization thresholds induced by the three diffusion processes are almost identical regardless of the selections of different PDFs . In this sense the PDFs have almost no influence on the onset of synchronization while the threshold amplitudes are merely determined by the spectral densities . This can be comprehended from the view of energy since the identical spectral densities of the three diffussion processes embody the same total power .
Two generalized Duffing systems subjected to a common stochastic excitation are studied. Three types of diffusion processes with identical spectral densities but different PDFs are taken as driving excitations. The synchronization thresholds induced by the three diffusion processes are almost identical. The synchronization thresholds are merely determined by the spectral densities but independent of the PDFs.
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We consider a system of two simple pendulums which interact by elastic forces according to Hookes law in the presence of the gravitational field . Analysis of global dynamics of the system by means of the Poincar sections the bifurcation diagrams and Lyapunovs exponents suggest its non integrability . We give an analytical proof of this fact . An analysis through differential Galois theory is done providing non integrability of the system for most of the values of the parameters . For a certain co dimension one in parameter space family we did not obtain integrability obstructions due to solvability of the first order variational equations of the Lam type . We show an application of the higher order variational equations for proving the non integrability in this case . As the final result we received that the system of two pendulums coupled by a spring is integrable only in two cases postulated in the main theorem of the work .
The system of two pendulums coupled by a spring is examined. The complexity of the model by means of Poincar sections the bifurcation diagrams and Lyapunovs exponents is presented. The proof of its non integrabiliry in the framework of differential Galois theory is given. For a certain co dimension one in parameter space family the higher order variational equations are used. Certain integrable cases are identified.
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This paper focuses on the vibration behaviors of a hollow shaft rotor system in presence of an open crack under inherent model uncertainties . Non probabilistic interval variables are used to represent the uncertain parameters which releases the high demands of probabilistic knowledge in the traditional methods . In modeling the shaft local stiffness matrix of the cracked element is derived by using the neutral axis method . The periodic response of the rotor system is solved by combination of the finite element method and the harmonic balance method . A simple mathematical function termed as the uncertain response surrogate function is constructed to estimate the vibrational response in various cases where different parametric uncertainties are taken into consideration . In order to verify the robustness and accuracy of the URSF the bounds of estimated response are compared with those obtained from the classical methods . Results show that the surrogate function has good accuracy and robustness providing an effective method and guidance for diagnosing crack in uncertain context .
The open crack in a hollow shaft is modeled based on relationships between crack depth and shaft radii. The surrogate function for the uncertain dynamic response is established using the interval descriptions. The accuracy and robustness of the interval methodology are validated by traditional sampling methods. The nonlinear dynamics are analyzed considering various uncertain parameters with different variations.
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When network users are interacting intensively by sending large amount of packets during window time handling and transmitting generated data can be challenging without violating quality of service as network resources are limited . As data packets flow has different regime and incoming packets arrival rate depends on users behavior we propose in this paper to analyze the predator prey interaction occurring between two users packets flows traveling network segment considering incoming packets as newborn and queuing packets as adult population using a modified Hutchinson interactive model . We focused our analysis on interaction outcome by performing qualitative studies of the proposed model . Theoretical analyses suggest adopting different queuing strategy and hybrid resources allocation by taking into account users behavior to enhance forwarding performance and improve transmission efficiency .
Handling and transmitting generated data can be challenging without violating QoS. Theoretical analysis suggested adopting different queuing strategy and hybrid resources allocation. Forwarding a given packet requires a decision making process that can be simple or extremely complex depending on the situation. In the proposed model we added Holling type II term in prey equation for better control of populations growth and time the predator needs to assimilate captured preys. Different aged packets can be handled by network segment during window time as far as allocated resources are not exhausted and network is not congested.
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In an anti Hermitian linear system all energy eigenvalues are purely imaginary and the corresponding eigenvectors are orthogonal . This implies that no stationary state is available in such systems . We consider an anti Hermitian lattice with cubic nonlinearity and explore novel nonlinear stationary modes . We discuss that relative population is conserved in a nonreciprocal tight binding lattice with periodical boundary conditions as opposed to parity time symmetric lattices . We study nonlinear nonrecipocal dimer triple and quadrimer models and construct stationary nonlinear modes .
We find that nonlinear stationary modes are available in nonlinear nonreciprocal lattices. We discuss that relative population is conserved in a nonlinear nonreciprocal dimer. We explore stability of modes for nonlinear extension of anti Hermitian lattices.
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Computing the attracting cycles via iterations near bifurcation parameters for the logistic map could be misleading for the beginner . The matter is the recognition of numerical convergence when it is not ultimately monotone thereby the true length of the limiting cycle as opposed to the impression of a double length . Among the tools used are Grbner basis Mathematica calculations and symbolic dynamics . We compute all the 209 superstable points of period length 11 . We also obtain the degree of these algebraic integers . Such computer assisted proofs are of philosophical interest too . The realization of a 5 periodicity as covered in this paper may resemble the discovery of quasicrystals a topic we briefly mention . Both share the symbolic dynamics aspect of self similarity . Finally for the antisymmetric cubic map we calculate some singly and some doubly superstable parameters .
Computing attracting cycles near bifurcation parameters for logistic and cubic maps. Realizing convergence to one limit point as opposed to numerical convergence to two. Computing all the 209 superstable points of period length up to 11 and their degrees. Calculating some singly or doubly superstable parameters for antisymmetric cubic map. Relations to philosophy of computer assisted mathematics and quasicrystals discovery.
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In this paper we investigate time fractional variable coefficient coupled Burgers equations for admissible form of variable coefficients under the condition of invariance . The reduced form of systems is obtained by using symmetries and ErdlyiKober fractional differential operators . Then the exact solutions of the reduced systems are obtained . Besides this using generalized Noethers theorem conservation laws are derived for corresponding fractional system .
Time fractional variable coefficient coupled Burgers equations for admissible form of variable coefficients under the condition of invariance is investigated. The reduced form of systems is obtained by using symmetries. the exact solutions of the reduced systems are obtained. Using generalized Noethers theorem conservation laws are derived.
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In this paper we consider a mean reverting stochastic volatility equation with regime switching and present some sufficient conditions for the existence of global positive solution asymptotic boundedness in
We show the existence of global positive solution to. for any initial value which extends the corresponding result in Mao etal. We gives the. th moment estimation asymptotically bounded in. th moment and the Lyapunov exponent of the solution. to. We present some sufficient conditions for that the process. determined by. is positive recurrent and admits a unique ergodic asymptotically invariant distribution.
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Nonlinear forced vibration of a single layer graphene sheets resting on a visco Pasternak foundation and exposed to a dual frequency excitation and a thermo magnetic field is the main objective of the present study . To obtain this goal based on nonlocal elasticity theory KelvinVoigt model nonlinear strain displacement relations are used to model the geometrical nonlinearity and governing equation of motion is derived . Then applying Galerkin technique the partial differential equation is transformed to the ordinary differential one . Derived equation of motion is analyzed and solved using multiple time scales method . Finally modulation equation under sub harmonic and super harmonic stimulation are studied . Emphasizing the effect of nonlinearity great attention is given to dual frequency excitation and results for nonlinear frequency response with respect to amplitude the phase angle and force amplitude for SLGS are also plotted . At the end results of this article are compared with results in the other researches . The results emphasize that the multi frequency excitation intensifies resonance behavior and jump phenomenon in SLGS .
Combinational excitation is responsible of multivaluedness in nonlinear frequency response. An increase in the foundation coefficients makes fundamental frequency response decay. Combinational force amplitude has a strong influence on resonance phenomenon. Dual frequency excitation can make the nonlinear behavior unpredictable and complex. Combinational excitation intensifies the effect of nonlinearity and jump phenomenon.
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We adopt Gamma renewal process to describe the synaptic input of Hodgkin Huxley neurons on a square lattice with no flux boundary . Based on the eigenfunction expansion of Laplace operator we show that the Hopf bifurcation point of the lattice is coincident with that of a single neuron model . By center manifold theorem and normal form theory we prove that the Hopf bifurcation is subcritical . And then we exhibit the effect of Gamma noise on the formation of spiral wave for the first time . It is revealed that the occurrence and elimination of the spiral wave can be controlled by adjusting the inhibitory excitatory ratio and noise parameters . Since spiral waves may contribute to both normal cortical and pathological activities the present investigation should be helpful for understanding the functional role of general neural noise .
We adopt Gamma renewal process to describe the synaptic input of Hodgkin Huxley neurons on a square lattice with no flux boundary. Based on the eigenfunction expansion of the Laplace operator we show that the Hopf bifurcation point of the lattice is found coincident with that of a single neuron model. Using center manifold theorem and normal form theory we prove that the Hopf bifurcation is subcritical. We exhibit the effect of Gamma noise on the formation of spiral wave for the first time. It is revealed that the occurrence and elimination of the spiral wave can be controlled by adjusting the inhibitory excitatory ratio and noise parameters.
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We consider merger of two parallel toroidal atomic Bose Einstein condensates with different vorticities in a three dimensional trap . In the tunnel coupling regime Josephson vortices emerge in the barrier between the superflows . When the barrier is gradually eliminated we observe essentially three dimensional evolution of quantum vortices which may include the development of the Kelvin Helmholtz instability at the interface between the rings in the framework of a weakly dissipative Gross Pitaevskii equation . An initially more populated ring carrying a persistent current can drag an initially non rotating less populated one into the same vortex state . The final state of the condensate crucially depends on an initial population imbalance in the double ring set as well as on the shape of the 3D trapping potential oblate or prolate . In the prolate configuration robust 3D
Quantization of superflows in coupled vertically stacked toroidal condensates is determined by two types of topological excitations vertically oriented vortex lines located in the central hole of the toroidal structure and radially oriented Josephson vortices rotational fluxons located in the low density region between the rings . The relaxation of the merging rings is driven by substantially 3D nonlinear dynamics of the vortex lines corresponding to persistent currents and Josephson vortices. The final state of the condensate crucially depends on an initial population imbalance in the double ring set as well as on the shape of the 3D trapping potential oblate or prolate. In the oblate axially squeezed configuration a ring with non zero angular momentum can impose its quantum state onto the originally non rotating ring only above a well defined critical value of the population imbalance. Instead of the development of the classical Kelvin Helmholtz instability at the interface of the merging persistent currents in a prolate potential trap sufficiently elongated in the axial direction we observe the formation of nonlinear robust hybrid vortex structures.
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General fractional calculus offers an elegant and self consistent path toward the generalization of fractional calculus to an enhanced class of kernels . Prabhakars theory can be thought of to some extent as an explicit realization of this scheme achieved by merging the Prabhakar function with the general wisdom of the standard formulation of fractional calculus . Here I discuss some implications that emerge when attempting to frame Prabhakars theory within the program of general fractional calculus .
Prabhakar fractional calculus. General fractional calculus. Reconciling Prabhakars theory with the scheme of general fractional calculus.
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This paper investigates Julia sets for a class of complex uncertain discrete systems involving Mittag Leffler functions . Julia sets of some classical maps are generalized and the influence of parameter
Fractional elements are introduced into integer order complex iteration maps. The influence of the parameter of the Mittag Leffler function on models Julia set and the sets fractal dimension is studied quantitatively. An adaptive control strategy for synchronization of Julia sets is proposed. The designed adaptive controller is simple and feasible.
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A dimensional nonlinear evolution equation is decomposed into three integrable dimensional models namely the nonlinear Schrdinger equation the complex modified Korteweg de Vries equation and the Lakshmanan Porsezian Daniel equation in different dimensions . On basis of a quartet Lax pair the general
The general Nth order rational solution of a 3 1 dimensional nonlinear evolution equation is derived by the Darboux transformation and limit approach. The doubly localized lumps with standard pattern and triangular pattern on a constant background in the x y y z and x z planes are shown. The fundamental rogue waves and the multi rogue waves on a constant background in the y z and x z planes are presented.
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In this paper we propose a delayed discrete SIR disease model with a saturate incidence rate and extend it to a patchy environment by taking the dispersal of susceptible individuals from one patch to the other into consideration . For the single patch model we establish the global threshold dynamics by the method of Lyapunov functionals . For the two patch model we show that the global dynamics of the disease free equilibrium two boundary endemic equilibria and the interior endemic equilibrium are determined by several threshold quantities . We also explore the impacts of the dispersal on the disease dynamics . Our interesting findings may provide some useful insights on how to properly manage the dispersal between different regions to control the spread of diseases .
Global threshold dynamics is obtained for a single patch discrete SIR disease model. Global dynamics of a two patch discrete disease model is also established. The impacts of dispersal between two patches on disease dynamics are fully explored.