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S1007570420301167 | Modulation instability rogue waves and spectral analysis are investigated for the nonlinear Schrdinger equation with the higher order terms . The modulation instability distribution characteristics from the sixth order to eighth order nonlinear Schrdinger equations are studied . Higher order dispersion terms are closely related to the distribution of modulation stability regime and | High order dispersion terms affect the distribution of the MS regime n order dispersion term corresponds to n 2 modulation stability curves. Parameter a determines the deflection direction deflection angle and width of rogue wave solution while. 6 determines the width and amplitude. Based on the spectral analysis rogue waves can be reduced to W shaped soliton so N order rogue waves corresponds to N order W shaped solitons. Arbitrary parameters a and. 6 affect the spectrum of first order solution for the sixth order nonlinear Schrdinger equation. Whether spectral analysis method or MI method their transition condition from rogue wave to W shaped soliton is consistent. |
S1007570420301179 | The study of an airfoil at low Reynolds number regime was found to be a typical problem where the inception of bifurcations leads the flow evolution from a stationary or periodic behaviour to a purely chaotic one . The present work extends the present literature where numerical investigations of the flow field past two dimensional symmetric airfoils were performed by fixing the incidence and changing the Reynolds number . Conversely here the Reynolds number was fixed at | Numerical study of a stalled symmetric airfoil at low Reynolds number. Discussion of bifurcation and non linear phenomena. Accurate numerical simulations performed with a Vortex Particle Method. Discussion of the time evolution of the forces with links to the wakes topology. Phase portrait diagrams are evaluated for the detection of limit cycles. |
S1007570420301180 | When a network is reconstructed from data two types of errors can occur false positive and false negative errors about the presence or absence of links . In this paper the vertex degree distribution of the true underlying network is analytically reconstructed using an iterative procedure . Such procedure is based on the inferred network and estimates for the probabilities | When a network is reconstructed false positive and false negative errors can occur. The vertex degree distribution of the underlying network is analytically reconstructed. An iteration procedure converges to the correct reconstruction. |
S1007570420301192 | The paper considers a new type of solutions for shunting inhibitory cellular neural networks strongly unpredictable oscillations . The conditions for the existence uniqueness and stability of the solutions are determined . Numerical examples are given to show the feasibility of the obtained results . | Shunting inhibitory cellular neural networks are under investigation. The models with strongly unpredictable inputs are considered. The line of periodic and almost periodic motions is continued with unpredictable oscillations. Existence and uniqueness of asymptotically stable strongly unpredictable solutions are proved. Illustrative examples and simulations to prove the feasibility of the results are provided. |
S1007570420301209 | Arrays of oscillators driven out of equilibrium can support the coexistence between coherent and incoherent domains that have become known as chimera states . Recently we have reported such an intriguing self organization phenomenon in a chain of locally coupled Duffing oscillators . Based on this prototype model we reveal a generalization of chimera states corresponding to the coexistence of incoherent domains . These freak states emerge through a bifurcation in which the coherent domain of an existing chimera state experiences an instability giving rise to another incoherent state . Using Lyapunov exponents and Fourier analysis allows us to characterize the dynamical nature of these extended solutions . Taking the Kuramoto order parameter we were able to compute the bifurcation diagram of freak chimera states . | Coexistence between complex spatiotemporal domains is numerically observed in locally coupled Duffing oscillator chain. A supercritical transition between localized complex spatiotemporal states. Characterization of the complexity of localized states as the energy injection increase. |
S1007570420301222 | In this paper the generalized trigonometric functions are modified for solving of the ordinary differential equation describing the motion of the strong nonlinear oscillator . The generalized trigonometric functions related to the p Laplacian which is the nonlinear differential operator are modified for solving equations with nonlinearity of any rational order . Based on the modified generalized trigonometric function and the known Krilov Bogoliubov method the new so called MGTF KBM method is developed . The method is applied for solving perturbed second order equations of oscillatory motion . As an example the oscillatory tooth motion excited with initial impulse force is considered . The tooth support system is modeled as a strong nonlinear oscillator . The analytically obtained vibration properties of the tooth are compared with experimentally obtained one and show a good agreement . | Modified generalized trigonometric function is solutions of nonlinear oscillators. New Modified Krylov Bogolubov method is developed. The tooth support motion is modelled as a strong nonlinear oscillator. Analytical and experimental results for tooth motion are in good agreement. |
S1007570420301234 | In this paper several efficient energy dissipative linear difference schemes are presented and analyzed for solving the coupled nonlinear damped fractional wave equations . First the weighted shifted Grnwald difference formula is used to approach the considered fractional system in space direction . Then we apply second order centered difference scheme and invariant energy quadratization Crank Nicolson scheme to discrete the resulting system in time direction respectively . Subsequently the convergence and stability of the proposed schemes are discussed . By using the discrete energy method and a cut off function technique it is proven that the suggested schemes attain the convergence orders of | It is significant to develop energy dissipative conservative numerical methods for simulating propagation of the coupled nonlinear damped space fractional wave equations in long time duration. We develop and analyze efficient linear energy dissipative difference schemes for the coupled nonlinear damped space fractional wave equations. The proposed finite difference methods are proved to be unconditionally convergent and stable. Some numerical results are exhibited to illustrate the physical effects of the damping terms and unconditional energy stability of the suggested schemes. |
S1007570420301246 | This paper solves the event triggered passivity problem for multiple weighted coupled delayed reaction diffusion memristive neural networks with fixed and switching topologies . On the one side by designing appropriate event triggered controllers several passivity criteria for MWCDRDMNNs with fixed topology are derived based on the Lyapunov functional method and some inequality techniques . Moreover some adequate conditions for ensuring asymptotical stability of the event triggered passive network are presented . On the other side we take the switching topology in network model into consideration and investigate the event triggered passivity and passivity based synchronization for MWCDRDMNNs with switching topology . Finally two examples with numerical simulation results are provided to illustrate the effectiveness of the obtained theoretical results . | Several event triggered passivity criteria for MWCDRDMNNs with fixed topology are proposed. Some conditions are obtained for ensuring passivity based synchronization of the MWCDRDMNNs. The event triggered passivity for switched MWCDRDMNNs are discussed. The obtained theoretical results are illustrated by two numerical examples. |
S1007570420301258 | The two dimensional shallow water equations with constant Coriolis parameter and variable topography bottom in mass Lagrangian coordinates are studied in this paper . The equations describing these flows are reduced to two Euler Lagrange equations . Group classification of these equations with respect to the function describing the topography of the bottom is performed in the paper . For some particular functions transformations mapping the two dimensional shallow water equations with constant Coriolis parameter into the gas dynamics equations of a polytropic gas with polytropic exponent | The studied equations are reduced to two EulerLagrange equations. The Lagrangian and Hamiltonian formalism of these equations is given. The transformations mapping the shallow water equations into the gas dynamics equations are found. Complete group classification of these equations with respect to the function describing the topography of the bottom is performed. |
S1007570420301271 | A chemostat is a widely used laboratory and industrial scale equipment for continuous culture of microalgae and other microorganisms under controlled conditions . Being a photosynthetic organism light and other nutrients are growth limiting for all microalgal species and thus optimization of external conditions is necessary to maximize algae harvest at a commercial scale . In this study we mechanistically formulate a cell quota based light dependent model of algae growth in a chemostat and study various mathematical properties of the model in addition to exploration of the parameter space for obtaining guidelines on biomass growth optimization . | Light dependent single nutrient limited cell quota based mechanistic model of algae growth in a chemostat is developed. Model solutions are positive and bounded. Sensitivity analysis reveals critical information on the impact of parameters and initial conditions on algae biomass productivity |
S1007570420301283 | The stability of a dynamical system against strong or weak perturbations is an important problem of nonlinear science especially when considering interconnected systems . In this work we use a concept known in the literature as | Stability of a power grid depends on the power distribution and the tripping time. Basin stability does not increase monotonically for shorter tripping time. It is best to not isolate the perturbed generator in heterogeneous power grids. |
S1007570420301295 | Nonlinear oscillators and networks can be synchronized by channel coupling for signal exchange while non coupling synchronization between chaotic oscillators can be obtained by applying the same stochastic disturbance for inducing resonance . For most of realistic dynamical systems physical energy and biophysical energy are pumped along the coupling channels and then the variables are regulated to present different modes in oscillation . In this paper a new photosensitive neuron is proposed to detect the dynamics in isolated neuron and synchronization stability by changing the illumination which can adjust the photocurrent across the branch circuit even no direct synapse coupling is applied . The generation of photocurrents with diversity is explained from physical viewpoint . Furthermore the collective responses of these photosensitive neurons in network are detected by calculating the synchronization stability and pattern formation . It is found that the spatial patterns in the network are dependent on the illumination . Uniform illumination can induce complete synchronization while non uniform illumination can develop rich spatial patterns . Furthermore uniform and stochastic photocurrents are imposed on all neurons to realize complete synchronization even synapse connection are removed from the network . These results can give potential guidance for designing functional neural circuits with potential application to identify optical signals as electronic eyes . | A new neural circuit composed of phototube is built for detecting optical signal. This new neuron model can sense and encode external illumination and is used as an artificial eye. This light dependent neurons can be synchronized without synapse coupling. Stochastic photocurrent driving can realize and enhance complete synchronization of network even synapse coupling is switched off. |
S1007570420301301 | In recent years there has been growing interest in nonlinear inverse problems of spectral analysis for integro differential operators . However in spite of permanently increasing number of works there are still no numerical results in this direction . The first aim of this paper is to fill this gap by developing an effective numerical approach to this class of inverse problems . The second aim is to prove the stability theorem which theoretically justifies our numerical method . As a model situation we consider one important and illustrative class of integro differential operators while the presented method can be extended to more complicated inverse problems . Our approach is based on reducing an inverse problem to some nonlinear integral equation and involves approximation of its solution by entire functions of exponential type . Concrete results of the numerical simulation are provided and discussed . | Global solution to a nonlinear inverse problem for integro differential operators is given. Stability of the inverse problem in appropriate metrics is established. An effective numerical algorithm is proposed for solving the inverse problem. Results of the numerical simulation are provided and discussed. |
S1007570420301313 | This paper presents a one dimensional superconducting photonic crystal refractive index biosensor with high sensitivity which consists of a periodic arrangement of superconductors and semiconductors . The biosensor has high sensitivity and accuracy in the refractive index range of 1.0 to 2.2 RIU below the critical temperature . The resonance wavelength and defect refractive index of the biosensor have a high linear correlation coefficient and the linear correlation coefficient of all experimental groups in this paper is higher than 0.999 . The sensitivity of the biosensor decreases with increasing temperature and when the external temperature increases from 80K to 134K the sensitivity decreases from 6.04396m RIU to 5.71703m RIU gradually . And then the performance of biosensor in blood component detection is researched by FDTD method . The result shows that the sensor has higher sensitivity and shows the same change law in the detection of refractive index changes within a small range such as blood components . When the external temperature is increased from 80K to 134K the sensitivity of the biosensor gradually decreases from 6.85789m RIU to 6.48073m RIU . | Ablood tissues detection biosensor based on superconducting photonic crystal working at low temperature is proposed. The performance of the biosensor is simulated by FDTD finite difference time domain method. The results show that it is feasibility and high performance of the biosensor in blood tissues detectionat low temperatures. |
S1007570420301337 | The nonlinear partial differential governing equations of the planar motion of a Z shaped structure are derived using Hamilton s principle . The 1 2 internally resonant global analytical mode shapes are validated by figure contrast and the modal assurance criterion . The partial differential governing equations are truncated into a two degree of freedom ordinary differential system with the validated resonant global analytical mode shapes and they are further investigated for internal and simultaneous primary resonances . The steady state responses are studied and numerical simulations of the system are performed . Complex nonlinear phenomena in the system such as jumps bifurcations quasiperiodic motion and chaos are observed under specific parameters . The parametric rule of these phenomena obviously depends on the accuracy of mode shapes . This work proposes a nonlinear analysis based on the quantitative validation of mode shapes which may provide new insights into the optimal design of the parameters and the precise control of the motions of Z shaped or other multibeam structures in engineering . | The resonant global analytical mode shapes are obtained by considering both the axial and transverse displacements. The analytical mode shapes are validated based on figure comparisons and MACs. The steady state responses of the system are solved as functions of the frequency and amplitude of the excitation. Periodic multiperiodic quasiperiodic and chaotic motions are analyzed numerically. The accuracy of the mode shapes plays an important role in determining the parametric rule of certain nonlinear phenomena. |
S1007570420301349 | Stationary density functions statistically characterize the stabilized behavior of dynamical systems . Instead of temporal sequences of data stationary densities are observed to determine the unknown transformations which is called the inverse Frobenius Perron problem . This paper proposes a new approach to determining the unique map from stationary densities generated by a one dimensional discrete time dynamical system driven by an external control input given the input density functions that are linearly independent . A numerical simulation example is used to validate the effectiveness of the developed approach . | One dimensional discrete time dynamical systems are inferred from stationary densities generated by the systems in the presence of input perturbation. The main assumption is that the stationary densities can be observed and estimated given arbitrary initial conditions. The unique stationary density function generated by a perturbed system exists corresponding to a specified input density function. The stationary density is dependent on the probability density function of an external control input given a transformation. A practical algorithm of determining the unknown transformation using stationary densities generated by a system with linearly independent input density functions is introduced. |
S1007570420301350 | In this paper we develop a mathematical model for the spread of the coronavirus disease 2019 . It is a new | Mathematical model for coronavirus disease that fits well the spread in China. New. SEIHRD model taking into account undetected infections. Validation of the model with the reported data on China. Estimation of errors when identifying parameters at early stages of the pandemic. Different scenarios to show the impact of undetected cases on the pandemic. |
S1007570420301428 | In this paper we discuss a diffusive predator prey model with nonlocality and delay . Stability and bifurcation analysis suggest that the joint impacts of the nonlocal term and delay result in instability of the positive constant steady state . Moreover steady state Hopf and steady state Hopf bifurcations and interactions of these bifurcations may occur under certain conditions . Normal forms of steady state Hopf and steady state Hopf bifurcations for a general reaction diffusion model with nonlocal effects and delay are derived . In numerical simulations spatially inhomogeneous steady states and periodic solutions and heteroclinic connections between these solutions are obtained . | Effect of spatial average and delay on the predator prey model is investigated. Conditions for stability steady state bifurcation and Hopf bifurcation are obtained. Algorithm of normal form of steady state Hopf bifurcation for system with spatial average and delay is derived. Spatiotemporal dynamical classification near the steady state Hopf bifurcation point is studied. |
S1007570420301441 | In this study we present a general formulation for the optimal control problem to a class of fuzzy fractional differential systems relating to SIR and SEIR epidemic models . In particular we investigate these epidemic models in the uncertain environment of fuzzy numbers with the rate of change expressed by granular Caputo fuzzy fractional derivatives of order | Optimal control problem governed by fuzzy fractional differential systems. Granular SIR and SEIR epidemic models are introduced. A Numerical Scheme to Solve Fractional Optimal Control Problems. An application of real data extracted from COVID 19 pandemic. |
S1007570420301453 | In this work a discretized two dimensional Leslie Gower prey predator model is investigated . The results for the existence and uniqueness and the conditions for the local asymptotic stability of the solutions are determined . It is also exhibited that the discrete system undergoes Neimark Sacker flip and fold bifurcation under certain conditions . The discretized system exhibits wide range of complex dynamical behavior viz . periodicity quasi periodicity and chaos with respect to different parameters . Further three control methods state feedback pole placement and hybrid control are deployed to control the chaos in the system . Under certain conditions chaos and bifurcation of the system are stabilized through the control strategies . The extensive numerical simulation is done to demonstrate the analytical findings . | A fractional ordered Leslie Gower prey predator model is studied. Jury stability test is applied to get certain conditions for occurrence of Neimark Sacker bifurcation flip bifurcation and fold bifurcation. A wide range of dynamics viz. periodic solution quasi periodicity and chaos is obtained. Three chaos control techniques State feedback pole placement and hybrid control are implemented in order to reduce the complexity of the system. State feedback and pole placement technique restore the stability for a certain range of parameters although hybrid control technique works effectively. |
S1007570420301544 | This study examines the stability and potential bifurcations of a stratified shear flow governed by the non rotating incompressible Boussinesq equation at a low Pclet number . For the ratio of the vertical scale to the horizontal scale of a stratified flow | It proves that a stratified shear flow governed by the non rotating incompressible Boussinesq equation at a low Pclet number becomes unstable as the Reynold number Re is above a threshold. There exists a supercritical Hopf bifurcation in the non rotating incompressible Boussinesq equation at the threshold. An upper boundedness of the threshold is derived. A stable periodic solution emerges in the non rotating incompressible Boussinesq equation at the threshold which describes an oscillating thermal convection in a highly stratified shear flow arising in the atmosphere or interior of many stellar systems. |
S1007570420301581 | This paper examines the state estimation issue of genetic regulatory networks including time delays and leakage delay term subject to unified dissipativity performance based on the Lyapunov functional approach . The main aim of the proposed state estimator is to access the true concentrations of the proteins and mRNAs which is explored based on the available output measurements . As a first attempt the generalized dissipativity concept is implemented for GRNs to generalizing the state estimation technique in the framework of linear matrix inequalities via an improved integral inequality together with the reciprocally convex inequality technique . Then the developed criterion ensures that the estimated error dynamics to be asymptotically stable and extended dissipative in addition to well monitored by the original dynamics via unified dissipativity performance . Finally an interesting simulation example as a synthetic oscillatory network of transcriptional regulators in | The generalized dissipativity concept is implemented for GRNs to estimate the state. The state estimation echnique proposed in the framework of LMIs via a novel improved integral inequality together with the RCI technique. The developed criterion ensures that the estimated error dynamics to be asymptotically stable and extended dissipative. |
S1007570420301611 | In this paper we propose a novel technique called dispersion transfer entropy to determine the information transfer and causal relation in the analysis of complex systems . Symbolization is used to solve the computational burden and noise sensitivity . To deal with the two major issues in symbolization generating partition and information loss we use the Ragwitz criterion to dynamically select parameters and utilize dispersion pattern to keep influential information . Moreover we extend DTE into the multivariate system and propose dispersion multivariate transfer entropy dispersion multivariate transfer entropy curve and dispersion partial transfer entropy . DMTE greatly weakens the influence of synchronicity and similarity in data on information transfer detection which is a breakthrough in solving the limitation of transfer entropy . DMTEC shows the evolution of causal relation over time and DPTE measures the direct causal effect between systems . These statistics can be combined to obtain a more comprehensive and accurate measurement of causality for multivariable systems . Also we apply these methods to simulation data as well as stock markets to verify the effectiveness of our methods . | We propose dispersion transfer entropy DTE to determine the information transfer and causal relation in the analysis of complex systems. Symbolization is used to solve the computational burden and noise sensitivity. We extend DTE into the multivariate system and propose dispersion multivariate transfer entropy DMTE and partial transfer entropy. DMTE greatly weakens the influence of synchronicity and similarity in data on information transfer detection. We apply these methods to simulation data as well as stock markets to verify the effectiveness of our methods. |
S1007570420301635 | In this paper we explore the phase space structures governing isomerization dynamics on a potential energy surface with four wells and an index 2 saddle . For this model we analyze the influence that coupling both degrees of freedom of the system and breaking the symmetry of the problem have on the geometrical template of phase space structures that characterizes reaction . To achieve this goal we apply the method of Lagrangian descriptors a technique with the capability of unveiling the key invariant manifolds that determine transport processes in nonlinear dynamical systems . This approach reveals with extraordinary detail the intricate geometry of the isomerization routes interconnecting the different potential wells and provides us with valuable information to distinguish between initial conditions that undergo sequential and concerted isomerization . | Analysis of the phase space structures associated to index 2 saddles with Lagrangian descriptors. Detection of reactivity regions for which the system undergoes distinct isomerization routes. Influence of coupling and symmetry breaking perturbations on the systems dynamical behavior. |
S1007570420301659 | In this paper the dynamical behaviors of an optimal velocity model with delayed feedback control of velocity difference is studied . By analyzing the transcendental characteristic equation the stable region of controlled OVM is obtained and the critical condition for Hopf bifurcation is derived . To stabilize the unstable traffic flow and control the bifurcations the definite integral stability method can be applied to determine the first stable intervals of time delay and feedback gain by calculating the number of all unstable eigenvalues of the characteristic equation . That is when the time delay and the feedback gain are chosen from the corresponding stable intervals the controlled OVM is stable and the stop and go traffic waves disappear . The numerical simulations in the case studies indicate that the proposed control strategy can suppress the traffic jams effectively and enhance the stability of traffic flow significantly . | The stability and bifurcation are analyzed in an OVM with time delayed feedback control of velocity differences. The first stable intervals of time delay and feedback gain are determined by using the improved definite integral stability method. The control method can suppress traffic jam by choosing feedback gain and time delay from the first stable intervals. The proposed method provides an effective and simple way to design controller. |
S1007570420301672 | This paper is dedicated to the resilient input to state stable filter design for nonlinear time delay systems subject to external disturbance input . Two types of time delay are taken into account . First novel analysis results on input to state stability for the filtering error systems are presented on the basis of the Lyapunov functional method . Both the Bessel Legendre inequality and the reciprocally convex combination approach are employed to reduce the conservatism of the present conditions . Then computationally tractable design strategies for the desired filters are developed via using a number of decoupling techniques . Finally two illustrative examples are given to demonstrate the effectiveness of the input to state stable filter approaches for the time variant delay case and the time invariant delay case respectively . | The issue of input to state stable filter design for nonlinear time delay systems subject to bounded external disturbance input and gain variations is considered. Novel analysis results on input to state stability for the filtering error systems are presented on the basis of the Lyapunov functional method. Computationally tractable design strategies for the desired resilient input to state stable filters are developed via using several decoupling techniques. |
S1007570420301684 | This paper is concerned with a general cross diffusion system modeling the population dynamics of two competitive predator and one prey with predator taxis . Firstly through the use of contraction mapping principle the Schauder estimates and | Considere the general three species two predators and one prey cross diffusion predator prey system with predator taxis. Investigate the existence uniqueness and boundedness of non negative classical solution. The global existence and uniqueness of non negative classical solution for this system are proved. Several numerical simulations are presented. |
S1007570420301726 | Cardiac myocyte electrical activity is traditionally approximated with ideal resistor capacitor circuit networks . However non ideal circuit components may provide a more realistic approximation of excitable cell behavior . Such non ideal circuit components are governed by fractional order dynamics and contribute capacitive memory effects to the excitable cell system . Our prior work has detailed the effects of cell membrane derived capacitive memory in a minimal cardiac model driven by voltage instabilities and capacitive memory has been shown to shorten the action potential duration and suppress a beat to beat alternation in the APD known as alternans . In this study we investigate the effects of memory in a biophysically detailed cardiac model that accounts for detailed representations of intracellular calcium cycling and transmembrane voltage dynamics . We perform simulations of varying fractional order and pacing cycle length and investigate conditions in which alternans is driven by either voltage or calcium mediated instabilities . We found that capacitive memory suppresses alternans when calcium mediated . Interestingly when mediated by voltage driven instabilities memory effects induced a calcium instability that in turn promoted alternans under most conditions . In summary capacitive memory due to fractional order dynamics alters electrical signaling in cardiac cells in a manner than may either promote or suppress instabilities . | Fractional order differential equations models can simulate non ideal electrical circuit components. Cardiac electrical models with non ideal circuit components account for physiological capacitive memory effects. Electrical instabilities known as alternans can arise in cardiac cells via voltage or calcium mediated mechanisms. Capacitive memory can either suppress or promote alternans depending on the underlying mechanism. |
S1007570420301738 | This paper reports a new chaotic system generated from the simplest memristor chaotic circuit by introducing a simple nonlinear feedback control input . The principal feature of the new system is that it has infinitely many equilibria and abundant coexisting attractors . The dynamic evolution of the system with respect to parameters and initial conditions is given to illustrate the existence of chaos and coexisting attractors . The circuit implementation is done for demonstrating the physical existence of the system . A microcontroller on Arduino Mega 2650 board is used to realize the system . Also the synchronization problem of the system is analyzed with the establishment of synchronization conditions based on the sliding mode control . | A new chaotic system with infinitely many coexisting attractors is presented. The dynamic behaviors of the new system are studied. The abundant coexisting attractors of the system are presented. The electronic circuit and microcontroller based implementation of the new system is studied. The consistence between the circuit outputs and the simulation results physically illustrates the existence of the system. The synchronization problem of the new system is studied by using the sliding mode control method and the corresponding synchronization conditions are established. |
S100757042030174X | This paper studies the leader following bounded consensus problem for multi agent systems in the present of denial of service attacks by means of event triggered control strategy . Due to the existence of DoS attacks the original system is transformed into a switched system with both stable and unstable modes . Moreover DoS attacks can be characterized by frequency and duration constraints under which the bounded consensus can be still guaranteed . It is shown that the duration constraint can be replaced by choosing appropriate mode dependent average dwell time for each subsystem . In order to obtain a smaller consensus bound and feedback gain matrices simultaneously an optimization approach is proposed . In addition the Zeno behavior that may be introduced by event triggered control is excluded . Finally a numerical example is provided to illustrate the bounded consensus can be still achieved under the co designed event triggered control strategy despite the presence of DoS attacks . | A novel explicit characterization of the frequency and duration properties of DoS attacks is proposed. The bounded consensus of leader following systems can be still achieved in the presence of DoS attacks. The system under event triggered control does not exhibit Zeno behavior by utilizing the new proposed method. |
S1007570420301751 | The one dimensional shallow water equations in Eulerian and Lagrangian coordinates are considered . It is shown the relationship between symmetries and conservation laws in Lagrangian coordinates and symmetries and conservation laws in mass Lagrangian variables . For equations in Lagrangian coordinates with a flat bottom an invariant difference scheme is constructed which possesses all the difference analogues of the conservation laws mass momentum energy the law of center of mass motion . Some exact invariant solutions are constructed for the invariant scheme while the scheme admits reduction on subgroups as well as the original system of equations . For an arbitrary shape of bottom it is possible to construct an invariant scheme with conservation of mass and momentum or alternatively mass and energy .. Invariant conservative difference scheme for the case of a flat bottom tested numerically in comparison with other known schemes . | Relationship between symmetries and conservation laws in Lagrangian potential coordinates and symmetries and conservation laws in mass Lagrangian variables is shown. For the one dimensional shallow water equations in Lagrangian coordinates with a flat bottom an invariant difference scheme is constructed which possesses all the difference analogues of the conservation laws mass momentum energy the law of center of mass motion. For an arbitrary shape of bottom invariant schemes with conservation of mass and momentum or energy are constructed. Some exact invariant solutions are constructed for the invariant scheme flat bottom case . Invariant conservative difference scheme for the case of a flat bottom tested numerically in comparison with other known schemes. |
S1007570420301763 | This paper investigates the robust stability of fractional order systems described in pseudo state space model with incommensurate fractional orders . An existing non conservative robust stability criterion for integer order systems is extended to incommensurate order fractional systems by using the generalized Nyquist Theorem . Some robust stability conditions for various uncertainty structures are proposed by employing the proposed criterion . Moreover we focus on the interval uncertainty structure to discuss the conservatism of the common methods . A numerical example is provided to investigate that how the fractional order of each pseudo state can affect the robustness of the system . The effectiveness of the proposed methods is compared by applying them on the problem of space tether deployment with fractional order control law . | A robust stability condition for incommensurate pseudo state space model is proposed. For some well known uncertainty structures some stability conditions are proposed. These conditions can be employed for different order systems without defining the additional pseudo state variables. The method for interval uncertainties does not lead to conservatism generated by reformulation of the interval uncertainty. Investiganing a numerical example leads to unexpected results about the robustness of fractional order systems. |
S1007570420301775 | In contrast to a non regulated market a regulated market can be defined as a market affected by external factors which cause abnormal behaviors in market prices . Nevertheless these behaviors are not enough to ignore the fundamental principles of finance while many econophysicists do so . In this paper it is considered that returns are driven by a finite moment log stable process in the most general form . Then a potential function is used to model the rest of the regulations . Consequently the pricing problem is formulated as an integral whose kernel can be found solving an inhomogeneous space fractional diffusion equation . Given the inhomogeneous equation with the Riesz Feller fractional derivative and the potential function a new path integral seems to be necessary to formulate the solution of the kernel equation . Thus a Generalized Fractional Path Integral will be derived and an Asymmetric Fractional Path Integral Monte Carlo algorithm will be developed to find the results . Finally a daily European call option is priced in a real market with a daily price limit rule and the maximum and minimum price for a typical contract is calculated as some example applications of the proposed approach . | Option pricing in a regulated market is formulated as an integral whose kernel can be found solving an inhomogeneous space fractional diffusion equation. A Generalized Fractional Path Integral is introduced to formulate the solution of the inhomogeneous space fractional diffusion equation. An Asymmetric Fractional Path Integral Monte Carlo algorithm is developed to solve the introduced generalized fractional path integral numerically. The effects of price limit mechanisms on the European call option price in a real market is discussed based on the proposed approach as an application of the introduced model. The maximum and the minimum price of a contract are calculated using the proposed approach as another application for the introduced model. |
S1007570420301799 | Alzheimers disease is a worldwide disease of dementia and is characterized by beta amyloid plaques . Increasing evidences show that there is a positive feedback loop between the level of beta amyloid and the level of calcium . In this paper stochastic noises are incorporated into a minimal model of Alzheimers disease which focuses upon the evolution of beta amyloid and calcium . Mathematical analysis indicates that solutions of the model without stochastic noises converge either to a unique equilibrium or to bistable equilibria . Analytical conditions for the stochastic P bifurcation are derived by means of technique of slow fast dynamical systems . A formula is presented to approximate the mean switching time from a normal state to a pathological state . A disease index is also proposed to predict the risk to transit from a normal state to a disease state . Further numerical simulations reveal how the parameters influence the evolutionary outcomes of beta amyloid and calcium . These results give new insights on the strategies to slow the development of Alzheimers disease . | Stochastic noises are introduced into the model of Alzheimers disease. Analytic conditions for stochastic P bifurcation are obtained. A formula is presented for the mean switching time from a mild impairment state to a pathological state. A disease index is proposed for the early warning of disease. The results provide insightful suggestions to design he strategies to slow the progression of disease. |
S1007570420301805 | We identify two types of dynamical bifurcations generated primarily by interactions of an invariant attracting submanifold with stable and unstable manifolds of hyperbolic fixed points . These bifurcation types inspired by recent investigations of mathematical models for walking droplet phenomena are introduced and illustrated . Some of the one parameter bifurcation types are analyzed in detail and extended from the plane to higher dimensional spaces . A few applications to walking droplet dynamics are analyzed . | Experimentalists often study the chaotic walking of droplets on a fluid bath. Discrete dynamical models of walking droplets exhibit a variety of bifurcations. Homoclinic heteroclinic bifurcations of the models lead to chaos. |
S1007570420301830 | A three dimensional nonlinear system modeling the enzymatic reaction of a substrate and two products is considered . We study how stochastic fluctuations of substrate input affect bistability regimes with coexisting equilibrium and limit cycle as well as birhythmicity with two coexisting cycles . For the analysis of noise induced phenomena we use an apparatus of confidence ellipsoids and tori constructed with the help of stochastic sensitivity function approach . Probabilistic mechanisms of the stochastic generation of complex mixed mode oscillatory regimes with spiking phases are discussed . It is shown that this phenomenon is accompanied by the transformation of regular nonlinear dynamics into chaotic . | Effects of random noise on the Goldbeter biochemical 3D model are studied. We analyze a noise induced bistability and birhythmicity. We apply the method of analysis based on confidence domains. Stochastic transformations from order to chaos are discussed. |
S100757042030191X | Derivatives of fractional order are introduced in different ways as left inverse of the fractional integral or by generalizing the limit of the difference quotient defining integer order derivatives . Although the two approaches lead to equivalent operators the first one does not involve the function at the left of the initial point where instead the latter forces the function to assume selected values . With fractional delay differential equations new problems arise the presence of the delay imposes to assign the solution not just at the initial point but on an entire interval . Due to the freedom in the choice of the initial function some inconsistencies with the values forced by the fractional derivative are possible and the operators may no longer be equivalent . In this paper we discuss the initialization of fractional delay differential equations we investigate the effects of the initial condition not only on the solution but also on the fractional operator as well and we study the difference between solutions obtained by incorporating or not the initial function in the memory of the fractional derivative . The exact solution of a family of linear equations is obtained by the Laplace transform whilst numerical methods are used to solve nonlinear problems the different results are therefore shown and commented . | Initial conditions for fractional delay differential equations are discussed. Effects of the initial conditions on the fractional derivative are studied. Exact solutions of linear fractional delay differential equations. Numerical approximations of nonlinear fractional delay differential equations are considered. |
S1007570420301945 | This paper reports a sequential design of linearly controlling a three dimensional quadratic system to a simple six dimensional hyperchaotic system with complex dynamics . By adding three linear dynamical controllers the resulting 6D system has no equilibrium and a hidden attractor which has four positive Lyapunov exponents . This paper focuses on the 6D system to reveal its unusual dynamics such as infinitely many singularly degenerate heteroclinic cycles and bifurcations from such singular orbits to hidden hyperchaotic attractors . Detailed numerical investigations are carried out including bifurcation diagram LE spectrum and phase portrait . Furthermore the system has multistability corresponding to three types of equilibria including no equilibrium and infinite non isolated equilibria . In particular we find that at least seven different attractors coexist when the system has one equilibrium line . Finally this 6D hyperchaotic system is verified by 01 test and a circuit . | Presents a new 6D hidden hyperchaotic system with four positive Lyapunov exponents which has no equilibrium or one equilibrium line or two equilibrium lines depending on different parameter values. Shows that the new system has many unusual complex dynamical behaviors such as infinitely many singularly degenerate heteroclinic cycles and bifurcations from such singular orbits to hidden hyperchaotic attractors. Shows that the system has multi stability corresponding to three types of equilibrium especially the coexistence of seven attractors when the system has one equilibrium line. Implements this system by 01 test and electronic circuit which displays very good agreement with the simulation result. |
S1007570420301957 | It has been a challenge to formulate network based control measures on infectious diseases especially on emerging diseases due to the complexity of the network topology . Generally isolating high degree nodes is one of the intuitive intervention measures . The final size and the epidemic duration are two vital evaluation indices of infectious diseases severity but the last one has not been explicitly calculated so far in network based models . Therefore in this paper we studied the effects of two measures of isolating high degree nodes at different timecomplete isolation and incomplete isolation on these two indices . We applied the reducing dimension method to convert the mean field model in networks into an equivalent and simpler low dimension model and then calculated the exact expression of the final size and the epidemic duration . We found that in complete isolation the final size always reduces but there exists an isolation time threshold of the epidemic duration in some cases before that such a strategy lengthens the epidemic duration and otherwise shortens that period . In contrast in incomplete isolation the epidemic duration always increases but there exists an isolation time threshold of the final size before which the incomplete isolation reduces the final size and otherwise increases the final size . This result provides a new insight into controlling infectious diseases in network . | We reduce a 3K dimension SIR mean field model to an equivalent low dimension model by the reducing dimension technique. We provide the exact expression of the final size and the epidemic duration based on the mean field model. We formulate two isolation measures of high degree nodes and analyze the effects of the measures on the final size and the epidemic duration. We find the crucial isolation time for the final size and the epidemic duration. |
S1007570420301969 | In this paper a system with energy harvester behavior is modeled by non smooth coupled oscillators subjected to harmonic and random excitations . A modified harmonic balance method is proposed to study the dynamics of the oscillators under harmonic driving . Then the probabilistic response of the system under bounded and colored noise excitations is tackled through the stochastic averaging method . We show that the proposed modified harmonic balance technique is very effective in parameters regime for which the system output waveform is nearly sinusoidal . In this parameters regime the harvester performance is improved for optimum nonlinear magnetic coupling coefficients and for weak nonlinearities and damping in the harvester mechanical part . Under random excitations we find in the weak parameters regime that the probability density functions for the coupled oscillators amplitudes illustrate a single peak mode and exhibit phenomenological transitions as the noisy excitations parameters vary . The mean output powers linearly increase with the colored noises intensities and the piezoelectric MOP especially shows a resonance effect as the bounded noise level increases . Contrariwise probed with Monte Carlo simulation we find that the system exhibits the stochastic P bifurcation for large parameters of coupling and nonlinearity parameters regime for which the harvester under purely harmonic driving demonstrates low performance . | Harmonic excitation strength is a critical parameter to improve the device efficacy. The device efficacy is optimum for certain nonlinear magnetic coupling coefficient. Single peak mode PDFs are observed in the weak parameter regime. Stochastic P bifurcation only appears in the hard coupling regime of the system. Piezoelectric MOP exhibits a resonance behavior as some bounded noise parameters vary. |
S1007570420301982 | A time fractional Allen Cahn equation with volume constraint is first proposed by introducing a nonlocal time dependent Lagrange multiplier . Adaptive linear second order energy stable schemes are developed for the proposed model by combining invariant energy quadratization and scalar auxiliary variable approaches with the recent L1 | A volume preserving time fractional Allen Cahn model is developed. Adaptive linear second order energy stable schemes are developed. The proposed adaptive time stepping algorithms are appropriate for accurately resolv ing the initial singularity of solution and for efficiently capturing the fast dynamics away initial time. |
S1007570420301994 | This paper is concerned with the coupled modified Korteweg de Vries equations . We derive infinite conservation laws through the Lax pair of the cmKdV equations . Through the analysis of the spectral stability with the conservation laws we obtain the nonlinear stability of breather solutions to the cmKdV equations . | The exact new breather type soliton solutions which is generalize of the breather solutions. We get stability tests via computing the generalized Weinstein conditions for the cmKdV breather solutions. According to the conservation laws we get variational characterization of breather solutions. Through the analysis of the spectral stability we present nonlinear stability of breather solutions to the cmKdV equations. |
S1007570420302008 | In this work we inspect the integrability of a natural Hamiltonian system interpreted physically as the motion of a particle in the Euclidean plane under the effect of conservative forces derived from a certain type of a non homogeneous potential . We announce the necessary conditions for its integrability by using the differential Galois theorem . We present three examples to clarify the applicability of the obtained results is easy and efficacious . Some of these examples restore the previous results in the literature and one of them gives a new integrable case describing a generalization of the well known Swinging Atwood machine . | A new theorem is introduced to study the integrability of a Hamiltonian system with certain type of nonhomogeneous potential. This new theory is more effective in studying the integrability of galactic potentials systematically. A new integrable problem which generalizes the Swinging Atwood machine is announced. |
S1007570420302021 | In this paper we investigate the mechanism of rotating waves in a ring of unidirectionally coupled Lorenz systems . Rotating waves in our Lorenz systems are special cases of rotating periodic solutions in nonlinear systems . Rotating periodic solutions as a generalization of periodic solutions have the form | The aim is to establish the Hopf bifurcation theorem of rotating periodic solutions in odd dimensional systems or systems coupled by multiple odd dimensional subsystems. Hopf bifurcation theorem of rotating periodic solutions can be used to analyze the mechanism of rotating waves in systems such as the unidirectionally coupled Lorenz systems. The rotating waves can be periodic quasi periodic or other types. |
S1007570420302045 | While COVID 19 is rapidly propagating around the globe the need for providing real time forecasts of the epidemics pushes fits of dynamical and statistical models to available data beyond their capabilities . Here we focus on statistical predictions of COVID 19 infections performed by fitting asymptotic distributions to actual data . By taking as a case study the epidemic evolution of total COVID 19 infections in Chinese provinces and Italian regions we find that predictions are characterized by large uncertainties at the early stages of the epidemic growth . Those uncertainties significantly reduce after the epidemics peak is reached . Differences in the uncertainty of the forecasts at a regional level can be used to highlight the delay in the spread of the virus . Our results warn that long term extrapolation of epidemics counts must be handled with extreme care as they crucially depend not only on the quality of data but also on the stage of the epidemics due to the intrinsically non linear nature of the underlying dynamics . These results suggest that real time epidemiological projections should include wide uncertainty ranges and urge for the needs of compiling high quality datasets of infections counts including asymptomatic patients . | Statistical predictions of COVID 19 infections performed by asymptotic distributions. Large uncertainties are found at the early stages of the epidemic growth. Uncertainties at a regional level highlight the delay in the spread of the virus. Long term extrapolation of epidemics counts must be handled with extreme care. Guidelines for real time forecasts considering possible source of errors. |
S1007570420302057 | Intraguild predation is a type of interaction in which a top predator simultaneously competes and predates an intermediate prey that shares a third prey species with the top predator . While common in nature most theoretical population dynamics models proposed in the literature predict that this three species interaction usually leads to extinction of the intermediate prey population . Predator induced defense as well as refuge mechanisms are widely seen in these systems and should be incorporated in IGP models to promote coexistence . With this aim we introduce a nonlinear response to the predation of IG predator on IG prey modelling both prey refuge and morphological defenses . The phase diagram of species coexistence is obtained as function of the attack efficiency and the degree of nonlinearity of the defense mechanisms . Further we show how the nonlinearity affects the equilibrium populations . We unveil that there is an optimal nonlinearity at which the convergence towards the stationary coexistence regime is the fastest . | Nonlinearity induced by the defense mechanism can induce the emergence of a wide regime of species coexistence. Very strong nonlinearities may lead to the extinction of the top predator population. There is an optimal nonlinearity at which the convergence towards the stationary coexistence regime is the fastest. |
S1007570420302203 | An error analysis of a super convergent discontinuous Galerkin method formulated in mixed form and applied to a general class of semi linear equations is presented . To reduce the computational cost at each time step the nonlinear term is approximated with a Lagrange interpolatory operator . Optimal convergence of order | Optimal convergence for both the primary and auxiliary variables. Super convergence of a post processed primary variable. Decoupling of nonlinear and diffusion terms by an operator splitting technique. Efficient preconditioner based on FSAI factorization. |
S1007570420302215 | Many vector borne disease epidemic models neglect the fact that in modern human civilization social awareness as well as self defence systems are overwhelming against advanced propagation of the disease . News is becoming more effortlessly accessible through social media and mobile apps while apparatuses for disease prevention are inclined to be more abundant and affordable . Here we study a simple hostvector model in which media triggered social awareness and seasonality in vector breeding are taken into account . There appears a certain threshold indicating the alarming outbreak the number of infective human individuals above which shall actuate the self defence systems for the susceptible subpopulation . A model where the infection rate revolves in the likelihood of limited medical access perceiving the disease as being easily curable and overwhelming hungrier vectors is proposed . Further discoveries are made from undertaking disparate time scales in human and vector population . The resulting slowfast system discloses notable dynamics in which solution trajectories confine to a slow manifold and the critical manifold before finally ending up at stable equilibria . How coinciding the slow manifold with the critical manifold enhances periodic forcing is also studied . The finding on hysteresis loops gives insights into how defining an alarming outbreak critically perturbs the basic reproductive number which later helps keep the incidence cycle on small magnitudes . | Epidemic model with periodic forcing and vectorhost lifespan ratio variation. Two models for the infection rate including social awareness among susceptible hosts. Existence behavior and stability of periodic solutions with respect to the periodic forcing amplitude and adiabatic parameter. Coinciding the slow and critical manifold giving birth to possible assimilation with lightly fluctuating data. Hysteresis loops and insights for possible control interventions. |
S1007570420302227 | Biological nervous system is very sensitive to external disturbances and appropriate stimulus is beneficial for improving neural function in the neural system . In this paper the effect of different external stimuli on chaotic dynamics in a Hopfield neural network with three neurons is explored . Mathematical model of the neural network is respectively established under three different cases namely without external stimulus with only electromagnetic radiation stimulus and with both electromagnetic radiation stimulus and multi level logic pulse stimulus . Under the three cases equilibrium points stabilities and attractors of the neural network are investigated carefully . The research results demonstrate that the neural network with periodic attractors can induce abundant chaotic attractors by imposing electromagnetic radiation on its one neuron . And when this neuron is simultaneously stimulated via electromagnetic radiation and multi level logic pulse the neural network can produce complex multi scroll attractors previously unobserved in Hopfield type neural networks . Numerical results are verified by hardware experiments effectively . Furthermore based on the Helmholtzs theorem the Hamilton energy of the neural network is calculated and analyzed . It is found that lower average Hamilton energy can be detected in the neural network when complexity of external stimuli is enhanced . These new findings could offer a new insight into the occurrence mechanism of some neurological diseases . | In this paper we investigate the chaotic dynamics of a Hopfield neural network under different types of external stimulus. The research results show that the neural network can exhibit different dynamical attractors under different external stimulus. Particularly the neural network simultaneously stimulated by electromagnetic radiation and multi level logic pulse can generate multi scroll attractors previously unobserved in Hopfield type neural networks. Furthermore the Hamilton energy of the neural network in different cases is calculated and analyzed and it is found that lower average Hamilton energy can be detected in the neural network when complexity of external stimulus is enhanced. Finally mathematical models of the neural network under with different stimulus are physically implemented by using simple analog circuit. |
S1007570420302239 | The rich dynamics of a system comprising of a Type I neuron coupled to a Type II neuron via an electrical synapse are explored in this paper . Diverse dynamical behaviour ranging from quiescence and periodic spiking to bursting and burst synchronization were observed for different coupling schemes . The bifurcation mechanisms underlying the various bursts observed were identified . We report a unique burst mechanism based on a focus node bifurcation occurring for bidirectionally coupled neurons . We attempt to understand the physical basis for the transitions from one burst pattern to another and also between the different aforementioned forms of dynamical behaviour observed on varying the coupling strength in both unidirectionally and bidirectionally coupled neurons . The various dynamical regimes of the coupled system are exhaustively studied and demarcated through parameter plots . Type I and type II neurons exhibit mutually phase synchronized burst patterns at large values of the coupling which tend towards complete synchronization on increasing the coupling strength . Such collective dynamical behaviour can have important implications in biological systems . | Coupled system of Type 1 and Type 2 neurons with different excitability mechanisms studied. Parameter space of coupled neurons exhaustively studied bursting mechanisms found. We report a unique burst mechanism based on a focus node bifurcation. Reasons underlying transitions from one burst pattern to another investigated. Type 1 and type 2 neurons show mutually phase synchronized bursts for strong coupling. |
S1007570420302240 | A study of primary and secondary instabilities in Rayleigh Bnard convection of water copper nanoliquid is made using a generalized two phase model . Boussinesq approximation and small scale convective motion are assumed to be valid . The Brownian motion effect is assumed to be negligibly small and a weak thermophoretic effect is included in the investigation . The parameter regimes for the existence of pitchfork Takens Bogdanov and Hopf bifurcations are reported . Small amplitude modulation is considered to derive the NewellWhiteheadSegel equation and using its phase winding solution the condition for the occurrence of Eckhaus and zigzag secondary instabilities are obtained . The influence of copper nanoparticles on the secondary instability region is reported . The travelling wave solutions for the NewellWhiteheadSegel equation are also presented . Oscillatory convection is not in general preferable in the problem yet in those cases where it can exist the necessary condition for the occurrence of Benjamin Feir instability is discussed . The present investigation sheds light on useful parameters ranges wherein a desired instability can be made to manifest depending upon the need of an engineering application . The Rayleigh Bnard convection can also be used as a rheometric tool for the measurement of viscosity and thermal diffusivity of the nanoliquid in a dynamic situation . | Existence of pitchfork Takens Bogdanov and Hopf bifurcations are reported for nanoliquids. Phase winding and travelling wave solutions of the Newell Whitehead Segel equation are obtained. Conditions for the occurrence of Eckhaus zigzag Benjamin Feir instabilities are presented graphically. The magnitude of influence of nanoparticles on primary instability is greater than its influence on secondaryinstability. A useful parameters ranges wherein a desired instability can be made to manifest are reported. |
S1007570420302252 | The icy moons are in the focus of the exploration plans of the leading space agencies because of the indications of water based life and geological activity observed in a number of these objects . In particular the presence of geyser like jets of water near Enceladus south pole has turned this moon of Saturn into a priority candidate to search for life and habitability features . This investigation proposes a set of trajectories between Halo orbits about Lagrangian points | Design of shadow heteroclinics between Halo orbits of Saturn Enceladus. Performance of shadow heteroclinics as science orbits is assessed. Ranges times of flight surface coverage and speeds are computed. Solutions offer long uninterrupted views of south pole at low speeds. |
S1007570420302264 | Structural vibrations are very common in aerospace and mechanical engineering systems where dynamic analysis of modern aerospace structures and industrial machines has become an indispensable step in their design . Suppression of unwanted vibrations and their exploitation for energy harvesting at the same time would be the most desirable scenario . The dynamical system presented in this communication is based on a discrete model of energy harvesting device realized in such a manner as to achieve both vibration suppression and harvesting of vibration energy by introducing the nonlinear energy sink concept . The mechanical model is formed as a two degree of freedom nonlinear oscillator with an oscillating magnet and harmonic base excitation . The corresponding mathematical model is based on the system of nonlinear nonhomogeneous Duffing type differential equations . To explore complex dynamical behaviour of the presented model periodic solutions and their bifurcations are found by using the incremental harmonic balance and continuation methods . For the detection of unstable periodic orbits the Floquet theory is applied and an interesting harmonic response of the presented nonlinear dynamical model is detected . The main advantage of the presented approach is its ability to obtain approximated periodic responses in terms of Fourier series and estimate the voltage output of an energy harvester for a system with strong nonlinearity . The accuracy of the presented methodology is verified by comparing the results obtained in this work with those obtained by a standard numerical integration method and results from the literature . Numerical examples show the effects of different physical parameters on amplitude frequency response amplitude base amplitude and time response curves where a qualitative change is explored and studied in detail . Presented theoretical results demonstrate that the proposed system has advanced performance in both system requirements vibration suppression and energy harvesting . | Nonlinear energy sink energy harvesting device based on coupled Duffing oscillators is proposed. Frequency amplitude and force amplitude responses are investigated by the incremental harmonic balance and continuation methods. Bifurcation points and unstable periodic solutions branches are detected. Short time energy localization to NES device is noticed. The influence of the nonlinear stiffness and resistance load on energy harvesting. |
S100757042030229X | This paper studies a contemporary event of the sunken Argentinian submarine ARA San Juan S 42 in November 2017 . The submarines wreckage was found one year later on the seabed off the southern Atlantic coast of Argentina with its imploded debris scattered on the seabed at the depth of about 900 meters under sea level . We develop computational mechanics modeling and conduct supercomputer simulations for this study using the versatile software LS DYNA as the platform . We first revisit underwater implosion phenomena by the test of pressurizing a plugged aluminum cylinder in a water tank and match the patterns of structural deformations as the important way to validate our computational methodology and model selections . Furthermore the radiations of the implosion shocks are computed and compared with those in the literature . Using a base model for the submarine we are able to perform event reconstruction for the underwater implosion of ARA San Juan S 42 . Our work can encompass the features of structural fracture and break up which were not included in the earlier studies . Furthermore we show that by adding ring stiffeners we can delay the onset of underwater implosion by increasing the tolerance of more water depth for the submarine . All the dynamic nonlinear implosion phenomena can be visualized by video animations obtained from our supercomputer simulations which are also compared with an artistically rendered video animation . | Addresses a contemporary event for which there is wide interest. Our approach is computational modeling using the advanced computer modeling software LS DYNA which is comprehensive and can help theory building. We are able to develop the right physics and then use supercomputer to simulate the PDEs and visualize the nonlinear dynamics of the underwater implosion process by video animations to see how the structural fracture and breakup taking place. By using LS DYNA our models and simulations can incorporate the fracture mechanical features which were mostly absent in previous works. We are able to provide an extensive set of graphical comparisons between computational mechanics and an artistically rendered movie which might eventually help movie making look even more realistic. Our work can facilitate future underwater vehicle designs to better withstand implosions in deep water. |
S100757042030232X | This paper is concerned with on the event triggered synchronization in fixed time for semi Markov switching dynamical complex networks with multiple weights and discontinuous nonlinearity . Firstly the principle of the global convergence in fixed time with respect to nonlinear systems with semi Markov switching is developed . Secondly in order to realize the global stochastic synchronization goal in fixed time a novel hybrid controller which is composed of the event triggered controller and the switching state feedback controller is designed . Under Filippov differential inclusion framework by applying Lyapunov functional method and inequality analysis technique the global stochastic synchronization conditions in fixed time are achieved in the form of linear matrix inequalities . In addition the upper bound of the stochastic settling time which is adjusted in advance by choosing the controller parameters is estimated accurately . Finally the correctness of the theoretical results and the feasibility of the designed controller are verified by an example . | A principle about the global stochastic stability in fixed time for the nonlinear system with semi Markov switching is developed see Lemma 2.1. The multiple weights and semi Markov stochastic process are introduced in CDNs the mathematics model with respect to semi Markov switching CDNs with discontinuous nonlinearity is proposed. The novel hybrid controller which is composed of the event triggered controller and the switching state feedback controller is designed. The global stochastic fixed time synchronization conditions are proposed in terms of LMIs. By adjusting the configuration of parameters in the designed controller the stochastic settling time can be determined to any expected value in advance. |
S1007570420302343 | New governing equation is obtained for nonlinear modeling of dynamics of hydrogen concentration in alloys . An influence of the nonlinear terms on the dynamics of hydrogen concentration is studied . A particular case is found when the governing equation admits exact kink shaped traveling wave solution . Numerical simualtion reveals different influence of the nonlinear terms arising in the equation due to different physical reasons . Qualitatively different effects such as arising of the tail behind the localized wave and formation of the counterpart wave are found . An influence of the polarity of the input on behavior of the localized wave of concentration is described . | New governing equation for the hydrogen concentration dynamics in alloys. Role of nonlinearities of different nature on the concentration wave. Polarity of the input affects the localized wave of concentration. |
S1007570420302355 | Hopping of individuals among distinct layers can induce inter layer coupling and consequently affect the spreading process in each layer of real world multilayer networks . We articulate a two layer network model where a fraction of nodes are inter layer travelers that can hop between layers . We develop a theoretical framework based on the quenched mean field approximation to accurately predict the epidemic thresholds and final states in both layers . Extensive numerical simulations on synthetic and empirical networks demonstrate that in the general setting where the structures of the two network layers are asymmetric intense hopping can lead to simultaneous epidemic outbreak in both layers . In general the impacts of hopping on the spreading dynamics in the two layers can be quite distinct . As the inter layer coupling strength is increased the epidemic threshold of the denser layer increases monotonically while for the sparser layer a surprising non monotonic behavior of the threshold with a minimize value arises . Another finding is that as a result of hopping recurrent outbreaks can occur in the sparser layer providing a plausible explanation for the phenomenon of multiple outbreaks observed from real health data . | We develop a theoretical framework to depict our network model with inter layer travelers and it works well. Intense hopping can lead to simultaneous epidemic outbreak in both layers. Inter layer hopping plays a double sword role in epidemic spreading in that they can either enhance or suppress the process. Recurrent outbreaks can occur as a result of inter layer hopping. |
S1007570420302379 | In this paper we first propose a general strategy to implement the Perfectly Matched Layer approach in the most standard numerical schemes used for simulating the dynamics of nonlinear Schrdinger equations . The methods are based on the time splitting Bao etal . or relaxation Besse schemes in time and FFT based pseudospectral discretization method in space . A thorough numerical study is developed for linear and nonlinear problems to understand how the PML approach behaves for a given scheme . The extension to the rotating Gross Pitaevskii equation is then proposed by using the rotating Lagrangian coordinates transformation method Antonelli etal . Bao etal . Garca Ripoll etal . some numerical simulations illustrating the strength of the proposed approach . | Implementation of PMLs in the framework of standard numerical methods to simulate nonlinear Schrdinger and Gross Pitaevskii equations. Analysis of the accuracy of the various methods. Extension to fast rotating GPE with high nonlinearity. |
S1007570420302380 | In this paper a new and efficient mechanism to compute the normal forms for 1 1 resonant Hopf bifurcation is developed . For a vector field given by ordinary differential equations by assuming that eigenvalues at an equilibrium point are purely imaginary double and non semisimple the mechanism provides a direct method to calculate the coefficients for the normal forms . In particular we present the following results a simple direct method to determine a basis of the complementary spaces for the Lie transform a simple direct method to determine the projection of any vector in | A simple direct method to determine a base of the complementary spaces for the Lie transform is given. The normal forms for vector field with double purely imaginary eigenvalues with geometric multiplicity one are considered. Explicit formulas for the normal forms coefficients with three unfolding parameter is given. Using this method the normal form for the non semisimple 1 1 resonance Hopf bifurcation can be given easily. |
S1007570420302409 | In this paper a periodic Chikungunya model with temperature and rainfall effects is proposed and studied which incorporates time dependent extrinsic incubation period time dependent maturation delay asymptomatic and symptomatic infectious humans . Two threshold parameters for the extinction and persistence of mosquitos and the virus are derived respectively the mosquito reproduction number | A periodic Chikungunya model with temperature and rainfall effects is studied. Time dependent maturation delay and extrinsic incubation period are incorporated. Infected humans are divided into symptomatic and asymptomatic compartments. Neglecting rainfall seasonality and asymptomatic compartment infection may be overestimated. Numerical simulations are done with data of the largest outbreak of Brazil in 2017. |
S1007570420302422 | Diffusion processes occurring in a myriad of systems sparkle great interest in understanding their general properties and applications . In this work we investigate a broad set of diffusive systems that can be governed by a generalized diffusion equation and subjected to a surface that can promote sorption and consequently desorption thus releasing the particles to the bulk . The general bulk equation used here can reproduce different diffusive regimes among them those described by the Cattaneo equation or by a fractional anomalous diffusion . The equation related to the processes on the surface incorporates non Debye relaxations which can be used to model non exponential relaxations commonly found in biological or fractal systems . The solutions are obtained by using the Green function approach and show a rich class of behavior that can be related to anomalous diffusion . | We investigate diffusive systems governed by a generalized diffusion equation. The sorption desorption modelling incorporates non Debye relaxations. The processes on the surface incorporates non Debye relaxations. We obtain solutions in terms of the Green function approach. We obtain a rich class of behavior that can be related to anomalous diffusion. |
S1007570420302434 | It was recently demonstrated that 2D Townes solitons in two component systems with cubic self focusing which are normally made unstable by the critical collapse can be stabilized by linear spin orbit coupling in Bose Einstein condensates and optics alike . We demonstrate that 1D TSs realized as optical spatial solitons in a planar dual core waveguide with dominant quintic self focusing may be stabilized by SOC like terms emulated by obliquity of the coupling between cores of the waveguide . Thus SOC offers a universal mechanism for the stabilization of TSs . A combination of systematic numerical considerations and analytical approximations identifies a vast stability area for skew symmetric solitons in the systems main and annex bandgaps . Tilted solitons are unstable spontaneously evolving into robust breathers . For broad solitons diffraction represented by second derivatives in the system may be neglected leading to a simplified model with a finite bandgap . It is populated by skew antisymmetric gap solitons which are nearly stable close to the gaps bottom . | One dimensional Townes like solitons in the system with quintic attraction may be stabilized by an effective spin orbit coupling SOC . We realize the stabilization mechanism in a model of on a planar double core optical waveguide with the quintic self focusing SOC being emulated by obliquity of the coupling between the cores. The system supports families of stable skew symmetric solitons in the systems bandgaps. |
S1007570420302446 | In this paper a physical interpretation of the fractional order derivatives effects in a jerk system based on Unstable Dissipative Systems and a Saturated Non Linear Function is presented . The system is electronically implemented in Multisim development platform for a 9 scrolls attractor generation . The behavior is analyzed trough the Detrended Fluctuation Analysis Probability Density Function bifurcation diagrams and the implementation of a geometrical analysis of the phase space . The changes that the system undergoes when a fractional order are analyzed . The results show that when the fractional integration orders are considered the areas of the generated attractor are modified with respect to the integer order dynamic . The long range correlations in the system are also modified because of the fractional orders . Besides a particular phenomenon in the equilibrium points preference occurs which is induced when the fractional integration order is applied in only one of the state variables . | Approach to a Fractional Order Derivatives FOD physical interpretation. Modification in the equilibrium point preference because of the FOD. Calculation of the attractor area in the. phase. Quantification of changes in the statistical properties of the system. A FOD changes the system vector field as a system control parameter |
S1007570420302458 | We highlight the existence of a topological horseshoe arising from an apriori stable model of the binary asteroid dynamics . The inspection is numerical and uses correctly aligned windows as described in a recent paper by A. Gierzkiewicz and P. Zgliczyski combined with a recent analysis of an associated secular problem . | The secular motions of binary asteroid system interacting with a planet are analysed. The perihelia of the ellipses of the asteroids afford stable unperturbed motions. A planet orbiting outside and coming close to the asteroids has a perturbing effect. The flow is reduced to a discrete map. Its phasespace is depicted. A topological horseshoe is constructed providing the existence of symbolic dynamics. |
S100757042030246X | We present a comprehensive study of nonlinear resonant modal energy scattering and passive vibration suppression in a linear cantilever beam with vibro impact nonlinear energy sinks attached to it . It is well known that vibro impacts are a strong source of non smooth nonlinearity resulting in rapid and intense multi scale energy scattering from low to high frequencies in the modal space of the beam . We present a direct correlation between such low to high frequency nonlinear energy scattering induced by vibro impacts and vibration suppression of the beam vibrations under both sweep and constant frequency harmonic excitations . In particular we study the intensity of the collisions between the tip of the beam and the particles of the VI NESs by means of an event driven method based on an explicit variable time step integration scheme and relate the dynamics of the integrated beam VI NES system to the induced resonant energy scattering from low beam modes to higher ones . On this basis the effects of the mass ratio and clearance between the absorber and the beam on the resonant energy scattering are presented . Our aim is to perform predictive design of the VI NESs for effective and robust vibration mitigation of the beam response . To this end we perform optimization studies on the mass ratio and clearance between the absorber and beam for the case of single and multiple VI NESs and identify regions of optimal suppression . Besides since the single VI NES is only effective in a limited frequency and amplitude range as its dynamics is energy dependent using multiple VI NESs with optimized parameters can extend the frequency range of effective vibration suppression rendering the resulting vibration mitigation more robust to variations of the applied excitations . | An event driven method based on an explicit variable step integration scheme is used. The VI NES collisions are classified into two categories according to their intensity. The effects of the mass ratio clearance on the resonant energy scattering are given. Optimization studies for single and multiple VI NESs systems were performed. The advantages of multiple dissimilar VI NESs on vibration suppression are given. |
S1007570420302471 | Population persistence and extinction are the most important issues in ecosystems . In the past a few decades various deterministic and stochastic mathematical models with Allee effect have been extensively studied . However in both population and disease dynamics the question of how structural transitions caused by internal or external environmental noise emerge has not been fully elucidated . In this paper we introduce a semi analytical method to explore the asymptotically convergent behavior of a stochastic avian influenza model with Allee effect . First by introducing noise to the model we observe numerically a significant transition from bistability to monostability . Next a corresponding Fokker Planck equation is obtained to analytically describe the probability density distributions with long time evolution in order to reveal the transition characteristics . Ratio of the approximately convergent probabilities for the two key equilibria derived from the FPK equation confirms the stability transition observed by previous numerical simulations . Moreover bifurcation analysis in two important parameters demonstrates that noise not only reduces the parametric zone of sustaining bistability but also drives the system to exhibit different monostabilities which correspond numerically to population persistence and extinction at different parametric intervals respectively . Furthermore noise induces higher probabilities for the system to sustain persistence instead of extinction in this model . Our results could provide some suggestions to improve wildlife species survival in more realistic situations where noise exists . | Aiming at the cross disciplinary field of the influence of stochasticity on epidemic problems our paper focuses on the stability transition different from previous studies which mostly dedicate to stability sustaining. With a semi analytically method our systematic explorations with key parameters demonstrate that noise has brought great changes to the dynamic behaviors of the biological system. Noise not only highly reduces the domain of parameters for sustaining bistablility but also drives the system to exhibit different monostabilities which refers to population persistence or extinction respectively at different parametric intervals. |
S1007570420302483 | In this paper we explore by means of the method of Lagrangian descriptors the Julia sets arising from complex maps and we analyze their underlying dynamics . In particular we take a look at two classical examples the quadratic mapping | Development of an effective scalar diagnostic to explore the phase space of complex maps. Analysis of the dynamics generated by archetypal exmaples of rational functions and their Julia sets. Algorithm capable of revealing simultaneously external rays equipotentials and laminations. |
S1007570420302501 | Enhancing and essentially generalizing previous results on a class of dimensional nonlinear wave and elliptic equations we apply several new techniques to classify admissible point transformations within this class up to the equivalence generated by its equivalence group . This gives an exhaustive description of its equivalence groupoid . After extending the algebraic method of group classification to non normalized classes of differential equations we solve the complete group classification problem for the class under study up to both usual and general point equivalences . The solution includes the complete preliminary group classification of the class and the construction of singular Lie symmetry extensions which are not related to subalgebras of the equivalence algebra . The complete preliminary group classification is based on classifying appropriate subalgebras of the entire infinite dimensional equivalence algebra whose projections are qualified as maximal extensions of the kernel invariance algebra . The results obtained can be used to construct exact solutions of nonlinear wave and elliptic equations . | We develop the theory of equivalence groupoids of classes of differential equations. A new version of the algebraic method of group classification is suggested. Notions of regular and singular cases of Lie symmetry extensions are introduced. We perform group classification of a class of nonlinear wave and elliptic equations. |
S1007570420302513 | This study addresses the nonlinear forced vibration of a deep curved microbeam with a noncontact actuator . The photostrictive actuator is subjected to an ultraviolet switching excitation and the governing equations are derived based on the couple stress theory . The von Krmn geometric nonlinearity is utilized to obtain the fundamental equations of thin curved beams in a curvilinear coordinate system . According to the type of boundaries inextensional condition is applied as a new strategy in such a structure to obtain solution analytically . By using the Galerkin method the equation of motion is discretized and reduced to the ordinary differential equation . Nonlinear analysis is then carried out on the reduced order equation by employing the multiple scales method . Based on the obtained results for the first time it is reported that qualitative and quantitative response of a deep curved beam is highly affected by the geometrical characteristics and the micro interactions . It is found that considering the deepness term | The nonlinear forced vibration of a curved beam via the couple stress theory. Nonlinear equation is solved analytically by employing the multiple scales method. The effects of geometrical characteristics on the nonlinear behaviour are studied. The Influence of micro interactions are evaluated. The considerable effect of the deepness term on the nonlinear response is investigated. |
S1007570420302562 | A dimensional fifth order integrable model the fifth member of the Kadomtsev Petviashvilli hierarchy is investigated . The Lax pairs and the bilinear form of the system lead to multiple soliton solutions . Applying the velocity resonance conditions to the multiple soliton solutions various types of soliton molecules such as the soliton molecules breather molecules and breather soliton molecules are presented . Moreover the interactions among the molecules are also investigated . | With the help of the Hirotas bilinear method we obtain the N soliton solutions and the Lax paris of KP5 equation. By means of the velocity resonance condition we derive the soliton molecules and breather molecules for the KP5 equation. We also investigate abundant interaction structure among solitons breathers soliton and breather molecules. |
S1007570420302574 | In this paper periodic orbits in the nonlinear dynamical system with a fixed point vortex in a periodic flow are investigated . Under the influence of periodic perturbations in the phase space an infinite number of nonlinear resonances with elliptic and hyperbolic periodic orbits arise . It is shown that these orbits exist even with completely destroyed resonant islands . In the perturbed system all periodic orbits with periods up to | Analysis of nonlinear resonances of the KAM and non KAM nature genetic relationship between different orbits. Using the example of a Hamiltonian system with 3 2 degrees of freedom it is shown that all elliptic orbits are destroyed by the universal cascade of period doubling bifurcations. The complex interaction of the hyperbolic orbits of the secondary resonances with the elliptic orbit of the primary resonance is demonstrated. It is shown that other bifurcation scenarios can be common to different orbits in addition to the universal period doubling cascade. |
S1007570420302598 | We study the synchronization critical coupling in the Kuramoto model of globally coupled oscillators analyzing natural frequencies distributed according to unimodal functions . Its is shown that asymmetric distributions can lead to a nonmonotonic critical transition when we modify some of their parameters . In particular we explore the case in which the natural frequencies are given by the log normal distribution . This case presents an interesting behavior in which synchrony vanishes with the increase in dispersion of natural frequencies but the continuous increase in dispersion may also recover part of the synchronization . Our numerical results are compared with analytical predictions based on self consistent equations . | The phase transition in the Kuramoto Model of globally coupled oscillators was investigated. It is shown that asymmetric distributions may lead to a nonmonotonic critical transition when we modify some of their parameters. The numerical evidence of a nonmonotonic critical threshold was predicted by the selfconsistence equations. |
S1007570420302628 | The fractional Klein Kramers equation describes the process of subdiffusion in the presence of an external force field in phase space and incorporates a fractional operator in time of order | The numerical methods are positivity preserving being in agreement with the physical properties of the problem. Physical boundary conditions are taken into account and its implementation is done in order to preserve the positivity. The accuracy lost due to the presence of boundaries is recovered using nonuniform meshes. |
S100757042030263X | In this paper we numerically investigate the space fractional nonlinear damped wave equation . We construct a novel high accuracy dissipation preserving finite difference scheme by using the new fourth order fractional central difference operator . Thanks to the toeplitz like differentiation matrix we further raise the computation efficiency of the proposed scheme by fast Fourier transform . Moreover we obtain the error estimate of our proposed scheme in | We propose a new fourth order dissipation preserving difference scheme for space fractional nonlinear damped wave equations. Our proposed fourth order scheme can generate the full toeplitz matrix it is convenient for us to speed up the matrix vector multiplication by fast Fourier transform. We obtain the. and. norm estimates which are discussed for two dimensional high dimensional space fractional nonlinear damped wave equations. We obtain the convergence analysis of fully discrete scheme without any restriction on step size ratio. Our proposed scheme performs more robust than some existing schemes for conserving dissipation preserving law. |
S1007570420302653 | A novel integrable asymmetric coupling of the Ablowitz Kaup Newell Segur system was generated by the completion process of the integrable coupling . We proved the Liouville integrability of the AKNS integrable coupling by deriving its bi Hamiltonian structures applying the variational identity . Nextly we investigated the generalized symmetry and infinitely many conservation laws by Hereman method for the integrable coupling system considered in this paper . Finally we presented the explicit solutions of the resulting integrable coupling system by constructing Darboux transformation for the first time . | New multi component asymmetric AKNS equations is constructed first from the completion progress of integrable couplings. For the first time we set up the N fold darboux transformation whichis constrained of the asymmetric model. Some integrable properties are studied in detail such as generalized symmetry and infinity conservation laws. The exact solutions of the asymmetric equations by way of completionare established. |
S1007570420302677 | Using asymptotic methods we investigate a local in a steady state neighbourhood behavior of solutions in the FermiPastaUlam model . Basing on the formalism of the normalization method we got special nonlinear evolution equations . The dynamics of these equations substantially defines the behavior of solutions of original equations . We made the conclusions about the interaction of waves moving in different directions . | developed the methods of local analysis of dynamics. studied the interaction of waves moving in different directions. got special evolution nonlinear equations to describe the original equation dynamics. |
S1007570420302689 | We investigate throughout this paper the effect of inhomogeneity on the propagation of solitons in ferromagnetic systems governing the magnetization evolution in a magnetic medium . Indeed we focus our attention on a nonlinear evolution equation derived by M. Saravanan and A. Arnaudon 2018 Phys . Lett . A | An integral modified KdV equation is considered. The KdV equation is solved for the solitons solutions using perturbation technique. The effect of inhomogeneity is studied and show deformed soliton excitation. |
S1007570420302707 | The objective of the presented article is to investigate the nonlinear dynamics and vibration of a simply supported fluid conveying pipe coupled with a geometrically nonlinear absorber as well as the occurrence of the targeted energy transfer phenomena in the system . In addition given the sensitivity of passive nonlinear absorbers performance to uncertainties in design and aleatory parameters such as the initial excitation of the primary system the optimal design of the absorber in presence of uncertainties is also examined in this paper . The absorber consists of two linear springs a lightweight mass and one linear damping configured in a particular formation and is coupled to the pipe in grounded and ungrounded configurations . It was indicated that the absorber can perform as a tuned mass damper nonlinear energy sink or a modified NES based on the bifurcation parameter value and finding the optimal type of the absorber is left to the optimization solver without any preceding knowledge of the physics of the system . It is illustrated that the stability of the pipe and the absorber effectiveness is reduced by increasing the inside flow velocity . Moreover the efficiency of the absorber slightly dependents on the density of the inside fluid . The results show that the stochastic optimally designed absorber can nonlinearly resonate with the pipe over extensive frequency ranges which leads to a synchronized motion of the pipe and absorber . In this situation a significant irreversible energy pumping from the pipe to the absorber may occur that make the motion localizes to the absorber and reduce the amplitude of the pipe for a wide range of initial excitation and fluid velocity . Also comparing the present work to other similar works yields a great result . | Vibration control of a pipe with a nonlinear absorber is presented. The nonlinear dynamic behavior of the system is investigated. It is possible for the absorber to perform as a TMD NES or modified NES. Ungrounded configuration is much more efficient than the grounded one. The optimal absorber can perform with high efficiency in a broadband range. |
S1007570420302720 | The quasi threshold phenomenon in Higgins model with mono stability driven by Gaussian white noise is investigated . The initial excitation phase is identified as escaping event with a specific trajectory defined as the quasi threshold . In the limit of weak noise a group of differential equations governing the optimal exit path quasi potential and exponential prefactor are deduced via WKB approximation . Results show that the optimal path approaches the quasi threshold with a nearly tangent way and almost follows the deterministic flow subsequently in the quasi potential plateau making it analogous to the bistable system . Numerical experiments verify not only the results of the optimal path but also the ones of the optimal fluctuational forces . Then the difference between the practical exit location and the position with minimal quasi potential is also revealed by including the exponential prefactor into the expression of exit location distribution . Finally the mean first passage time is evaluated theoretically with the secondary order approximation taken into consideration . These findings and computations shed light on exploring underlying qualitative mechanism and quantitative feature of excitation behaviors in biological systems . | Defining the most sensitive trajectory as the quasi threshold in mono stable system. Analyzing excitability and quasi threshold phenomenon in terms of large deviation theory. Discussing the behaviors of exit paths based on the computation of quasi potential. Approximating exit location distribution and mean first passage time analytically. |
S1007570420302744 | Fractional phase field models have been reported to suitably describe the anomalous two phase transport in heterogeneous porous media evolution of structural damage and image inpainting process . It is commonly different to derive their analytical solutions and the numerical solution to these fractional models is an attractive work . As one of the popular fractional phase field models in this paper we propose a fresh lattice Boltzmann method for the fractional Cahn Hilliard equation . To this end we first transform the fractional Cahn Hilliard equation into the standard one based on the Caputo derivative . Then the modified equilibrium distribution function and proper source term are incorporated into the LB method in order to recover the targeting equation . Several numerical experiments including the circular disk quadrate interface droplet coalescence and spinodal decomposition are carried out to validate the present LB method . It is shown that the numerical results at different fractional orders agree well with the analytical solution or some available results . Besides it is found that increasing the fractional order promotes a faster evolution of phase interface in accordance with its physical definition and also the system energy predicted by the present LB method conforms to the energy dissipation law . | A time fractional Cahn Hilliard model equipped with the Caputo derivative is studied. A fresh lattice Boltzmann method for the fractional Cahn Hilliard equation is proposed. The proposed model accurately describes interface dynamics with the fractional effect. The predicted system energy conforms to the energy dissipation law. |
S1007570420302756 | In this paper we consider an important kind of fractional partial differential equations namely multi term time fractional mixed sub diffusion and diffusion wave equation . The crucial importance of the considered equation is due to the fact that it generalizes some substantial types of fractional differential equations that can be widely used in describing many real life phenomena some of these equations are the time fractional sub diffusion time fractional diffusion wave and time fractional diffusion equations . In this study the 2D multi term time fractional mixed sub diffusion and diffusion wave equation is transformed to its integrated form with respect to time . An extension of the operational matrix of second order derivative to the 2D case is used in combination with the operational matrix of fractional order integrals and the time space spectral collocation method to reduce such equations to systems of algebraic equations which are solved using any suitable solver . As far as the authors know this is the first attempt to deal with 2D multi term time fractional mixed sub diffusion and diffusion wave equation via a spectral approach . Numerical examples are provided to highlight the convergence rate and the flexibility of this approach . Our results confirm that nonlocal numerical methods are best suited to discretize fractional differential equations as they naturally take the global behavior of the solution into account . | The first attempt to apply a spectral method for the two dimensional multi term time fractional mixed sub diffusion and diffusion wave equation is introduced. The operational matrix of second order derivative is extended to the two dimensional case. The time space spectral collocation method is used for the integral form of the two dimensional multi term time fractional mixed sub diffusion and diffusion wave equation. High accuracy results may be obtained using a low number of Legendre polynomials. Various numerical experiments are performed to demonstrate the validity and superiority of the proposed algorithm. |
S1007570420302768 | In this paper we use a phenomenological field theory model to study the first order phase transition from the lamellar phase to the inverse hexagonal phase in specific lipid bilayers . The model is described by a real scalar field with potential that supports both symmetric and asymmetric phase conformations . We adapt the coordinate and parameters of the model to describe the phase transition and we show that the model is capable of correctly inferring the fraction of the inverse hexagonal phase in the phase transition suggesting an alternative way to be couple to experimental techniques generally required for H | We consider the lamellar to the inverse hexagonal phase transition. A field theory model is used to study first order phase transition in lipid bilayers. The proposed model correctly predicts the fraction of the inverse hexagonal phase. A new scalar field model supporting asymmetric kinklike configurations is obtained. |
S100757042030277X | In this paper we focus on investigating a dimensional generalized breaking soliton equation with five model parameters which contains a lot of important nonlinear partial differential equations as its special cases . Firstly the integrability features of two special cases of the gBS equation are clarified . Secondly a general method is established to construct solutions formed by a combination of | Some integrable properties of gBS equation are clarified. A systematic method is provided to construct multiple cosh solutions. The non static lump solution and its analysis are presented. The real lump soliton solutions and other exact solutions are obtained. |
S1007570420302811 | Lyapunov exponent is a widely used tool for studying dynamical systems . When calculating Lyapunov exponents for piecewise smooth systems with time delayed arguments one faces a lack of continuity in the variational problem . This paper studies how to build a variational equation for the efficient construction of Jacobians along trajectories of a delayed nonsmooth system . Trajectories of a piecewise smooth system may encounter the so called grazing event where the trajectory approaches a discontinuity surface in the state space in a non transversal manner . For this event we develop a grazing point estimation algorithm to ensure the accuracy of trajectories for the nonlinear and the variational equations . We show that the eigenvalues of the Jacobian matrix computed by the algorithm converge with an order consistent with the order of the numerical integration method therefore guaranteeing the reliability of the proposed numerical method . Finally the method is demonstrated on a periodically forced impacting oscillator under the time delayed feedback control . | Calculation of Lyapunov exponents of piecewise smooth DDEs is studied. We focus on the grazing event at where trajectory approaches discontinuity surface. A grazing estimation algorithm is proposed to improve computational accuracy. The method is validated on an impacting system under the delayed feedback control. |
S1007570420302823 | Nonlinear mesoscopic materials exhibit anomalous elastic nonlinearity in which fast and slow dynamics effects are mixed up . The former is an instantaneous nonlinear phenomenon due to the explicit strain dependence of velocity and damping . Slow dynamics is a non equilibrium effect governed by the dependence of the linear modulus and Q factor on the dynamic strain level when excited at constant strain the sample properties vary in time until they reach a new equilibrium state . When excitation is removed again slowly in time the system recovers its original viscoelastic properties . The goal of this contribution is to show how slow dynamics might affect fast dynamics measurements and thus point out that care should be given to all time scales of the experiment e.g . lag time between amplitude change and acquisition duration of the acquisition and relaxation time between successive measurements . | The different power law dependences of nonlinear indicators observed when slow dynamic effects are removed from the measurement using specific measurement protocols. The dependence of the nonlinearity strength on the measurement time. The longer is the acquisition time the stronger is the cumulative effect of self conditioning with a consequent overestimation of the nonlinearity. The dependence of the amount of hysteresis given by the area of the loops observed for the dependence of the nonlinear indicator vs. amplitude in increasing decreasing amplitude protocols on the time scale of the experiment. |
S1007570420302835 | Positive and negative nonlinear integrable lattice hierarchies are established starting from a discrete matrix spectral problem with three potential functions particularly the corresponding Hamiltonian structures are presented respectively with the help of the trace identity all these facts show that these two hierarchies are integrable in Liouville sense . By using Lax pair we derive infinite number of conservation laws and | Construct positive and negative integrable lattice hierarchies and corresponding Hamiltonian structures. Derive the infinite number of conservation laws. Establish. fold Darboux transformations. Present explicit exact solutions and plot figures to illustrate the propagation of solitary waves. |
S1007570420302859 | The main goal of this paper is to understand the formation of hexagonal patterns from the dynamical transition theory point of view . We consider the transitions from a steady state of an abstract nonlinear dissipative system . To shed light on the formation of mixed mode patterns such as the hexagonal pattern we consider the case where the linearized operator of the system has two critical real eigenvalues at a critical value | Generic transitions resulting in the formation of hexagonal patterns is analyzed. All possible transition scenarios are classified using dynamic tansition theory. Applications of results to nonlinear dissipative systems is discussed. |
S1007570420302872 | In this project we study the periodic Dirichlet boundary value problem for a singularly perturbed reaction advection diffusion equation on the segment in case of discontinuous reactive and convective terms . Applying the boundary function method we construct the asymptotic approximation of the periodic solution with internal transition layer located in the vicinity of a curve of discontinuity of the mentioned terms . For the problem here we prove the existence of the periodic solution estimate the accuracy of the asymptotical approximation and investigate the stability of the periodic solution as solutions of the corresponding initial boundary value problems for the reaction advection diffusion equation . | The main characteristic of discontinuous singularly perturbed parabolic is that the second partial derivative is discontinuous on the both sides of the discontinuous curve. This characteristic leads to solution often feature a narrow internal layer region of rapid change near the discontinuous curve. Especially the value of the solution passing through the discontinuous curve is undetermined. We can use the smooth connection method to make the solution smoothly passes through discontinuous curve and determine the passing position. This is a new asymptotic method rather than the simply generalization of the methods of corresponding continuous system. |
S1007570420302914 | Delay Sobolev equations are a class of important models in fluid mechanics thermodynamics and the other related fields . For solving this class of equations in this paper linearized compact difference methods for one and two dimensional problems of DSEs are suggested . The solvability and convergence of the methods are analyzed and it is proved under some appropriate conditions that the methods are convergent of order two in time and order four in space . In order to improve the computational accuracy of LCDMs in time we introduce the Richardson extrapolation technique which leads to the improved LCDMs can reach the fourth order accuracy in both time and space . Finally with several numerical experiments the theoretical accuracy and computational effectiveness of the proposed methods are further testified . | This paper deals with the numerical computation and analysis for nonlinear delay Sobolev equations. Linearized compact difference methods LCDMs are proposed for solving 1D and 2D nonlinear delay Sobolev equations respectively. The proposed methods are proved to be unique solvable and have secondorder accuracy in time and fourth order accuracy in space. An extrapolation technique is combined with LCDMs which improves the accuracy in time and fourth order accuracy in time can be achieved. Several numerical examples testify the theoretical results and the computational effectiveness of the proposed methods. |
S1007570420302938 | We propose and analyze a virus to cell and cell to cell infections HIV model that includes intracellular time delay and infection age structure where infection age specific conversion function is considered as the piecewise function related to infection period between initial infection and the formation of productively infected cells . Applying the theory of integrated semigroup and the Hopf bifurcation theory for semilinear equations with non dense domain we concern the Hopf bifurcation of the model . A non trivial periodic solution bifurcates from the positive equilibrium when bifurcation parameter passes through some critical values . The numerical results verify our theoretical conclusion and further demonstrate that intracellular time delay has a greater impact on the model but the impact of infection period on the model is hardly obvious . Additionally the sensitivity of the threshold parameter is also carried out by employing the Latin hyper cube sampling method and partial rank correlation coefficient techniques . | An HIV model that includes intracellular time delay and infection age structure is proposedand analyzed. We employ the integrated semigroup theory and Hopf bifurcation theory for semilinear e quations with non dense domain. A non trivial periodic solution bifurcates from the positive equilibrium. The numerical results verify our theoretical conclusion. The sensitivity of. is carried out by using the Latin hypercube sampling and partial rank correlation coefficient. |
S1040619020300208 | This study develops projections of future spending and savings from electricity efficiency programs funded by electric utility customers in the United States through 2030 based on three scenarios . Our analysis relies on detailed bottom up modeling of current state energy efficiency policies demand side management and integrated resource plans and regulatory decisions . The three scenarios represent a range of potential outcomes given the policy environment at the time of the study and uncertainties in the broader economic and state policy environment in each state . We project spending to increase to 8.6 billion in 2030 in the medium scenario about a 45 percent increase relative to 2016 spending . In the high case annual spending increases to 11.1 billion in 2030 and remains relatively flat in the low case . Our analysis suggests that electricity efficiency programs funded by utility customers will continue to impact load growth significantly at least through 2030 as savings as a percent of retail sales are forecast at 0.7 percent in the medium scenario and 0.98 percent in the high scenario . | In this study we project future spending from electricity efficiency programs funded by utility customers in the U.S. to increase to 8.6 billion in 2030 in the medium scenario about a 45 percent increase relative to 2016 spending. In the high case annual spending increases to 11.1 billion in 2030 and remains relatively flat in the low case 6.8 billion in 2030 . Our analysis suggests that electricity efficiency programs funded by utility customers will continue to impact load growth significantly at least through 2030 with incremental annual savings to increase to 28 and 38 terawatt hours TWh in 2030 in the medium and high scenario respectively. Several factors are critical to the future spending and savings trajectory of customer funded efficiency programs 1 impact of declining costs of electricity supply options 2 Federal standards and building codes will moderate savings opportunities for utility programs 3 state leadership drives institutional frameworks for energy efficiency and 4 program portfolios will need to evolve to continue capturing cost effective electricity savings. |
S1040619020301135 | The Ontario Energy Board recently heard an application from incumbent demand response providers claiming that changes to the system operators demand response only capacity auction to allow certain generators to participate were unjustly discriminatory . The claim was based on costs borne by demand responders when curtailed that would not be recovered without energy payments . Using basic economic theory this paper analyzes the implications of variable costs of demand response and how they should best be handled to preserve economic efficiency of dispatch . | Demand response providers who incur variable costs of curtailment should add these costs to Value of Lost Load. Basic economic theory confirms that such bids will contribute to efficiency and maximum gains from trade. Energy payments made to demand responders will incent inefficient demand reductions and create income transfers. |
S1040619020301160 | Exploiting the implementation of a Prepaid Electricity Program in the region of Antioquia we estimate the impact that switching to a prepaid program has on users energy consumption behavior . In particular we focus the analysis on those that are more vulnerable from a socio economic perspective . The results show that the new metering scheme and the information provision is associated with a decline in electricity consumption.This scheme allow users to improve their consumption paths while their access to public electricity services is guaranteed minimizing disconnection risks and the associated costs . | We analyze the impact that switching to a prepaid electricity program has on users energy consumption behaviour. Prepaid electricity consumption schemes supported by AMI can be used as an alternative demand response mechanism. This scheme gives the most vulnerable households a chance to self manage their consumption and demand electricity according to their income flow. Switched users improve their consumption paths while their access to public electricity service is guaranteed. |
S1083879119304781 | Development of autoimmune cytopenia after allogeneic hematopoietic cell transplantation is a serious complication requiring urgent intensification of immunosuppressive therapy . The pathophysiology and predictors of AIC are not completely understood . In this retrospective cohort analysis of 380 pediatric patients we evaluated the incidence outcomes and related various variables including immune reconstitution markers to AIC . Three hundred eighty patients were included of which 30 patients developed AIC in 1 2 or 3 cell lineages at a median of 133 days after HCT . Using multivariate analysis we found that chemo naivety before HCT acute graft versus host disease grades II to IV and serotherapy were associated with the development of AIC . Development of AIC was preceded by increased levels of IgM IgA and IgG . Immune profiles of total absolute lymphocytes were very similar between AIC patients and control subjects . However CD3 | Chemo naivety before HCT and serotherapy are predictors for developing AIC. aGVHD grades II to IV is a predictor for developing AIC. IgM IgG and IgA levels increase before development of AIC. AIC is a rare but severe complication after HCT. Recognizing AIC is challenging and treatment should begin as quickly as possible. |
S1083879119304975 | Peripheral blood stem cell transplantation is being increasingly performed as an alternative to bone marrow transplantation however PBSCT has not been proven to have equivalent outcome to BMT . We conducted a meta analysis to compare survival rates and treatment related complications between PBSCT and BMT for pediatric hematologic malignancies . We searched Medline Embase plus Embase classics and the Cochrane Central Register of Controlled Trials for the terms hematopoietic stem cell transplantation AND allogeneic transplantation AND children including randomized controlled studies and cohort studies without language limitations . We identified 7 of 5368 studies for inclusion in our meta analysis . The cohorts of these studies included a total of 4328 patients 3185 who underwent BMT and 1143 who underwent PBSCT . Five year overall survival was similar in the 2 groups 1.17 95 confidence interval .91 to 1.52 as was the 5 year event free survival . The incidences of nonrelapse mortality and chronic graft versus host disease were higher in the PBSCT group compared with the BMT group . This meta analysis found insufficient evidence to conclude that peripheral blood stem cells are equivalent to bone marrow . The results indicate that bone marrow can still be a preferred donor source for pediatric hematologic malignancies . | We report a meta analysis comparing survival rates and treatment related complications between peripheral blood stem cell transplantation PBSCT and bone marrow transplantation BMT for pediatric hematologic malignancies. Overall survival and event free survival were comparable in the PBSCT and BMT groups. The incidences of nonrelapse mortality and chronic graft versus host disease were higher in the PBSCT group compared with the BMT group. This meta analysis found insufficient evidence to conclude that peripheral blood stem cells are superior to bone marrow and the results indicate that bone marrow can still be a preferable donor source for pediatric hematologic malignancies. |
S1083879119305178 | CD19 targeted chimeric antigen receptor modified T cell therapy has shown excellent antitumor activity in patients with relapsed refractory B cell malignancies with very encouraging response rates and outcomes . However the late effects following this therapy remain unknown . Here we report late adverse eventsdefined as starting or persisting beyond 90 days after CAR T cell infusionin patients who survived at least 1 year after therapy . The median duration of follow up was 28.1 months . At last follow up 73 of patients were still alive and 24 were in ongoing complete remission . The most common late adverse event was hypogammaglobulinemia replacement observed in 67 of the patients with available data . Infection density was .55 infection 100 days at risk . The majority of the infections were treated in the outpatient setting and 5 necessitated admission to the intensive care unit . Subsequent malignancies occurred in 15 of patients including 5 with myelodysplastic syndrome . Among patients with ongoing CR and with no MDS 16 experienced prolonged cytopenia requiring transfusions or growth factor support . Graft versus host disease occurred in 3 of 15 patients who had undergone previous allogeneic hematopoietic cell transplantation . Most of the late events observed in this cohort were not severe and many could be related to previous or subsequent therapies suggesting a safe long term profile of CD19 targeted CAR T cell immunotherapy . | Hypogammaglobulinemia was the most common late event. Most infections were mild and treated in the outpatient setting. Subsequent malignancies occurred in 15 of patients. 16 of patients with ongoing complete remission and no myelodysplastic syndrome MDS experienced prolonged cytopenias. Graft versus host disease occurred in 20 of patients who underwent previous allogeneic hematopoietic stem cell transplantation. |
S1083879119305233 | Autologous stem cell transplant is the standard of care for patients with multiple myeloma . The clinical significance of peripheral blood T lymphocyte immunologic changes associated with ASCT is poorly understood . Here we evaluated T cell transcriptional messenger RNA profiles and immunophenotypes to correlate immunologic senescence exhaustion and anergy with clinical endpoints in a cohort of patients with MM undergoing ASCT . ASCT induced global transcriptional T cell changes and altered molecular levels of markers of T cell subtypes T cell activation and exhaustion . These included reduced CD4 CD8 ratio skewing toward the Th1 subset reduced expression of costimulatory receptors CD27 and CD28 heightened T cell activation and increased expression of immune modulatory molecules LAG3 and PD1 . Multicolor flow cytometry experiments confirmed altered circulating CD4 and CD8 subsets and skewing toward differentiated effector cells . Moreover ASCT promoted an exhausted immunophenotype in CD3 | Autologous stem cell transplant ASCT induces global transcriptional T cell changes and altered molecular levels of markers of T cell subtypes T cell activation and exhaustion in patients with multiple myeloma. High LAG3 transcript expression in T cells detectable as early as 3 months post transplant is associated with inferior clinical outcomes in patients with myeloma. ASCT affected soluble levels of molecules with immunomodulatory function by increasing plasma HVEM and TIM3. ASCT promotes an exhausted immunophenotype in CD4. cells and a senescent anergic immunophenotype in CD8. subsets. Future work targeting immune defects in multiple myeloma is warranted to augment or restore T cell responses using the next generation of immune checkpoint inhibitors. |
S1083879119305245 | Philadelphia chromosomelike acute lymphoblastic leukemia is a relatively new entity characterized by high cytokine receptor and tyrosine kinase signaling resulting in multiple downstream pathway stimulation . The standard diagnostic method gene expression profiling is not widely available . Efforts are ongoing to establish easy and clinically applicable diagnostic pathways to facilitate the accurate identification of these patients and thus enable a better understanding of the prognosis and outcomes with different treatment approaches . The rates of complete remission in ALL patients are consistently above 90 with the different induction protocols however maintaining remission depends on the risk group of the patient and consolidation therapy . Allogeneic hematopoietic cell transplant is particularly beneficial when the risk of relapse is very high and the expected complications with transplant are low . Data on the outcomes of allo HCT for Ph like ALL are scarce . In this article we review the published literature on outcomes of Ph like ALL patients treated using different therapeutic approaches and make recommendations about transplant consideration for these patients . | Ph like ALL is a relatively new entity. Data on the outcomes of allo HCT for Ph like ALL are scarce. Review of literature and recommendations about allo HCT for Ph like ALL patients are presented. |
S1083879119305300 | Treatment for AL amyloidosis aims to eradicate clonal plasma cells thereby disrupting the amyloid deposition causing organ damage . Risk adapted high dose melphalan plus autologous stem cell transplantation is an effective therapy . We conducted a prospective pilot analysis of a comprehensive approach using bortezomib and dexamethasone before and after RA ASCT in 19 patients . BD induction up to 3 cycles of bortezomib 1.3 mg m | We analyzed treatment with bortezomib and dexamethasone before and after risk adapted autologous stem cell transplantation. This comprehensive 3 phase regimen is safe for the upfront management of AL amyloidosis. We report deep including minimal residual disease negative durable remissions promoting organ recovery. |
S1083879119305580 | Allogeneic blood or marrow transplantation is a potentially curative therapy for patients with primary immunodeficiency . Safe and effective reduced intensity conditioning approaches that are associated with low toxicity use alternative donors and afford good immune reconstitution are needed to advance the field . Twenty PID patients ranging in age from 4 to 58 years were treated on a prospective clinical trial of a novel radiation free and serotherapy free RIC T cell replete BMT approach using pentostatin low dose cyclophosphamide and busulfan for conditioning with post transplantation cyclophosphamide based graft versus host disease prophylaxis . This was a high risk cohort with a median hematopoietic cell transplantation comorbidity index of 3 . With median follow up of survivors of 1.9 years 1 year overall survival was 90 and grade III to IV acute GVHD free graft failure free survival was 80 at day 180 . Graft failure incidence was 10 . Split chimerism was frequently observed at early post BMT timepoints with a lower percentage of donor T cells which gradually increased by day 60 . The cumulative incidences of grade II to IV and grade III to IV acute GVHD were 15 and 5 respectively . All aGVHD was steroid responsive . No patients developed chronic GVHD . Few significant organ toxicities were observed . Evidence of phenotype reversal was observed for all engrafted patients even those with significantly mixed chimerism or with unknown underlying genetic defect . All 6 patients with pre BMT malignancies or lymphoproliferative disorders remain in remission . Most patients have discontinued immunoglobulin replacement . All survivors are off immunosuppression for GVHD prophylaxis or treatment . This novel RIC BMT approach for patients with PID has yielded promising results even for high risk patients . | We designed a novel reduced intensity radiation and serotherapy free blood or marrow transplantation BMT platform. A high risk cohort of 20 primary immunodeficiency children and adults received BMT. Acute graft versus host disease GVHD rates were low no chronic GVHD occurred even with alternative donor use. Low toxicity and mortality were observed. All engrafted patients showed evidence of phenotype reversal. |
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