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S1007570419304472 | This paper explores the prime numbers in the perspective of complex systems using computational and information visualization resources . The PN are interpreted as features that characterize the outputs of a CS . Four distinct metrics are adopted to assess the differences between such objects namely the Canberra Euclidean Jaccard and Lorentzian distances and the information is treated with a multidimensional scaling algorithm . The MDS produces loci organized according with the objects features that are analyzed under the light of the emerging patterns . Additionally these patterns are explored in the Fourier domain under the point of view of fractional calculus . The representations constitute a new philosophy for tackling the challenging topic of PN using advanced scientific visualization . | We explore prime numbers as objects in a complex systems. The dissimilarity information between objects is measured by different metrics. The data are processed by multidimensional scaling algorithms. The multidimensional scaling loci are explored using the tools of fractional calculus. |
S1007570419304484 | The study of regular and chaotic Rayleigh Bnard convective motions in methanol and water is made . The stationary mode of convection is shown to be the preferred one at the onset of convection in the case of both the liquids . Using a higher order truncated Fourier series representation we arrive at the energy conserving penta modal Lorenz model and then the tri modal Lorenz model is obtained as a limiting case of it . To keep the study analytical the Ginzburg Landau model is derived from the penta modal Lorenz model . It is shown that the tri and the penta modal Lorenz models predict exactly the same results leading to the conclusion that the tri modal Lorenz model is a good enough truncated model for a weakly nonlinear study of convection . The Rayleigh numbers at which the onset of regular convective and chaotic motions occur are reported for both methanol and water . The behavior of the dynamical system is studied using the spectrum of Lyapunov exponents the maximum Lyapunov exponent the bifurcation diagram and the phase space plots . The Hopf bifurcation Rayleigh number is obtained analytically . It is shown that the thresholds for onset of regular and chaotic motions are smaller in the case of methanol compared to water . Another very important finding of the paper is to show the existence of a developing region for chaos before becoming fully developed . | Regular chaotic and periodic Rayleigh Benard convective motions in methanol and water are reported. The comparison of heat transport between water and methanol is presented. The merits of methanol and the demerits of water as coolants in thermal systems are documented. From the study it is evident that methanol is stable in regular and periodic regimes and quite vigorously active in the chaotic regime compared to water. The percentage of enhanced heat transport in water compared to methanol is just around 0.17 . The possibility of having a transition region between regular convection and chaotic motions is demonstrated. |
S1007570419304496 | Considering the strong non linear properties of rolling element bearings a new model for the dynamic analysis of rotor bearing system especially for the heavy load and high speed condition is proposed in this work . Two types of bearing stiffness are classified and analyzed with physical meanings based on the load deflection curves which can full preserve the geometric and kinematic nature of REBs for the vibration model . The improved numerical integration process based on 4th order Runge Kutta method is described in details . One type of cylindrical bearing with internal clearance is brought in for case study . Complicated non linear vibration behaviors caused by REBs instinct properties are observed . The effects from speed fluctuation unbalance forces external loads on the vibration responses of the system are investigated . This work may provide some references for the structure design vibration prognosis and other engineering applications of the rotor bearing system . | A dynamic model for rotor bearing system with strong nonlinearity is proposed. Two kinds of bearing stiffness are classified based on their different physical meanings. The numerical computation process based on improved Runge Kutta method is described in details. One type of cylindrical roller bearing is introduced for case study. Strong nonlinear phenomenon and behaviors are observed and discussed. |
S1007570419304502 | The kink instability of magnetohydrodynamics is believed to be fundamental to many aspects of the dynamic activity of the solar atmosphere such as the initiation of flares and the heating of the solar corona . In this work we investigate the importance of viscosity on the kink instability . In particular we focus on two forms of viscosity isotropic viscosity and anisotropic viscosity . Through the detailed analysis of magnetohydrodynamic simulations of the kink instability with both types of viscosity we show that the form of viscosity has a significant effect on the nonlinear dynamics of the instability . The different viscosities allow for different flow and current structures to develop thus affecting the behaviour of magnetic relaxation the formation of secondary instabilities and the Ohmic and viscous heating produced . Our results have important consequences for the interpretation of solar observations of the kink instability . | Anisotropic and isotropic viscosity are compared. The choice of viscosity model has a strong effect on magnetic relaxation. Anisotropic viscosity enhances reconnection rate and Ohmic heating. Overall heating is reduced when using anisotropic viscosity. |
S1007570419304514 | The main concern of this paper is to develop and analyze the high order RungeKutta convolution quadrature method for obtaining the numerical solution of nonlinear fractional integro differential equations with weakly singular kernels . We first study the existence and uniqueness of solutions for the original problem . Then the convergence and stability results of the RKCQ method are obtained . Finally some numerical experiments are reported to illustrate the effectiveness of the proposed schemes . | The Runge Kutta convolution quadrature methods for solving of non linear Volterra integral equations with weakly singular kernels is offered. We study the existence and uniqueness of solutions for the original problem. The convergence and stability analysis of the new developed schemes is presented. We prove that the rate of convergence of the proposed algorithm is |
S1007570419304526 | Most previous studies on stochastic resonance have focused on models without boundaries . However the dynamics of the confined systems are affected by space limitations which exert unique effects on the reaction diffusion and SR behavior of systems . Some subsequent studies have discussed the SR like phenomena in the 2D confined spaces in the presence of uneven boundaries . However few reports have been published the response and SR of Brownian particle movement in a 1D space restricted by constant boundaries . In this paper we considered an overdamped bistable system excited by a periodic driving force and an additive Gaussian white noise in the presence of constant restricted boundaries and studied the response and SR phenomena of this confined system from the perspectives of limit cycle and potential function . The presence of the baffles changes the shape of the system potential function and limit cycles thereby changing the dynamic properties of the system . Therefore the SR of the confined system also undergoes significant changes compared with the original unconfined bistable system . It pointed out a criterion for SR of the confined overdamped bistable system on the basis of the relative position of limit cycles of the deterministic confined system and baffles . | Few reports have studied the SR of Brownian particle movement in a 1D space restricted by constant boundaries. It pointed out a criterion for SR of the confined overdamped bistable system on the basis of the relative position of limit cycles of the deterministic confined system and baffles. Compared with the unconfined system an appropriately sized boundary may introduce significant SR with shaper peak and even introduce SR to the unconfined systems without SR. The presence of the boundaries may also introduce superharmonic frequency components and the classical SR residual SR and double peaks SR all appear in the superharmonic frequencies. |
S1007570419304538 | In this paper the forced convective heat transfer of viscoelastic fluid flow around a circular cylinder at a low Reynolds number is studied numerically . The effect of viscous dissipation on the problem is modeld which is the main innovative aspect of present study . The PhanThienTanner model is used as the nonlinear constitutive equation . To avoid divergence and stabilize the numerical process in high elastic cases the log conformation approach is used . The results indicated that the Nusselt number monotonically increases with increasing elasticity number retardation ratio Prandtl number and Brinkman number in a wide range . Both drag reduction and drag enhancement were seen in the numerical results . In high elastic flow regime due to the increased storing nature of viscoelastic fluid compared to the dissipative nature drag coefficient | The non linear PTT model describes the viscoelastic behavior of fluid. Effect of temperature dependency of fluid properties are studied. Effects of El Pr and Br on flow and heat transfer are studied. Heat transfer enhancement and drag reduction are seen with elastic effects. Two correlations are proposed for drag coefficient and Nusselt number. |
S100757041930454X | In this paper a dimensional Hirota Satsuma Ito like equation is introduced based on the dimensional Hirota Satsuma Ito equation . Bcklund transformation and corresponding exponential function solutions are deduced by virtue of the Hirota bilinear form . The lump solutions are constructed and the interaction phenomena between a lump wave and multi kink waves are discussed . The lump wave may turn up in different positions and can be swallowed by multi kink waves which means that the collision is non elastic . Finally the dynamical behavior of the interaction phenomena is numerically simulated . | A 3 1 dimensional Hirota Satsuma Ito like equation is proposed which can describe the wave motion in fluid dynamics and shallow water. Bcklund transformation and corresponding exponential function solutions are de duced via the Hirota bilinear form. Interaction phenomena between a lump wave and multi kink waves are discussed and numerically simulated which show the collisions are non elastic. The lump wave may turn in different positions and can be swallowed by multi kink waves. |
S1007570419304551 | In this paper the dynamic properties of a stochastic model are studied through the stability of ergodic invariant measures on invariant sets . The threshold analysis of strong stochastic persistence and extinction is given . Moreover the necessary and sufficient condition for persistence and extinction in the sense of time average is give for a special critical state . The stochastic bifurcation phenomenon of the model is studied from the viewpoint of dynamic bifurcation . The main conclusions are verified by examples and numerical simulations . In addition the intra specific competition of two species are considered in this paper the importance of intra specific competition is also illustrated by theoretical results . The results can also provide a theoretical basis for the modeling of stochastic population models . | The stability of ergodic invariant measures on invariant sets are used to study dynamic properties. The threshold of strong stochastic persistence and extinction is obtained. Stochastic bifurcation phenomenon is studied from the viewpoint of dynamic bifurcation. Numerical simulations are given to explain main results. |
S1007570419304563 | We experimentally numerically and theoretically characterize the effectiveness of incommensurate excitations at suppressing chaos in damped driven systems . Specifically we consider an inertial Brownian particle moving in a prototypical two well potential and subjected to a primary harmonic excitation and a suppressory incommensurategeneric excitation . We show that the effective amplitude of the suppressory excitation is minimal when the impulse transmitted by it is near its maximum while its value is rather insensitive to higher order convergents of the irrational ratio between the involved driving periods . Remarkably the number and values of the effective initial phase difference between the two excitations are independent of the impulse while they critically depend on each particular convergent in a complex way involving both the approximate frustration of chaos inducing homoclinic bifurcations and the maximum survival of relevant spatio temporal symmetries of the dynamical equation . | This paper studies the effectiveness in chaos suppresing of incommensurately related drivings acting in a archetypal nonlinear oscillator. It has been characterized experimental numerical and theoretically the dependence of regularized behaviours with the parameters of the system. It has been shown the fundamental role played by the impulse transmitted by the suppressory excitation. |
S1007570419304575 | The importance of guides has been paid more attentions by managers of large buildings during the establishment of evacuation plans . Considering the inaccuracy of perceptual information by pedestrians and guides this paper chooses the fuzzy logic theory which is good at processing qualitative knowledge and experience with unclear boundaries to investigate the problems of guide selection by informed followers and exit selection by guides . Two factors namely the followers normalized distance to the guide and the normalized local pedestrian density around the guide are taken into consideration when determining to select which guide for informed followers . Guides normalized distance to the exit and the normalized density around the exit are chosen as the input variables of the fuzzy inference system to assist in deciding which exit to choose for guides . On the basis of the proposed methods pedestrian evacuation dynamics is studied through analyzing the simulation data of desired and actual velocities trajectories and outflow from each exit from which the effectiveness of exit selection method proposed in this paper can be explained . Evacuation efficiency due to the limited visibility guide quantity and exit attribute is further investigated . Simulation results indicate that evacuation efficiency does have a close relationship with the building visibility guide quantity and exit width . To a certain extent more guides greater visibility and wider exit are conducive to a large proportion of pedestrians to realize safety evacuation . Moreover the exit is suggested to design at the middle position of a wall which is better to the traffic of guided groups . | Guided crowd evacuation dynamics is investigated. Guide selection by informed followers and exit selection by guides are studied. Evacuation efficiency due to the limited visibility guide quantity and exit attribute is investigated. |
S1007570419304605 | This paper provides sufficient conditions for input to state stability of two interconnected nonlinear impulsive systems whose jump instants are not necessarily identical . Unlike prior results each subsystem is allowed to possess stabilizing or destabilizing flows . In this regard a candidate exponential input to state stable Lyapunov function is constructed for the overall system . Then by bounding the trajectory for each possible combination of impulsive subsystems sufficient conditions are presented which ensure input to state stability of the interconnected system . Furthermore to render the newly derived conditions less conservative the coefficients of the candidate exponential ISS Lyapunov function of each subsystem are considered to be time varying . The applicability of the theoretical outcomes is verified through some numerical examples . | Input to state stability of two interconnected impulsive systems with a class of non coincident impulse sequences is studied. The coefficients of the candidate exponential ISS Lyapunov function of each subsystem are considered to be time varying. The newly derived conditions demand DT RDT constraints on impulse sequences to ensure input to state stability. Unlike prior results each subsystem is allowed to possess stabilizing or destabilizing flows. |
S1007570419304617 | In the present work the problem of quantization of a robot via the Schrodinger equation with Jerk Levy noise and the wave function plots is analyzed . Quantum average and quantum fluctuation of the trajectory positions are displayed . It is observed that the quantum robots are molecules whose link angles can be varied resulting in changing chemical properties thus justifying the importance of this work also in physics of biological engineering . we have also made computations on the statistics of the wave function as well as transition probabilities between two stationary states . The quantum analysis has been based on using time independent perturbation theory to evaluate the approximate evolution operator of the unperturbed robot . | Eigen values Eigen function of 2 link quantum robot without torque are computed using first order time independent perturbation theory. Wave function evolution of 2 link robot are obtained using Dyson series approximation with Poisson process integrals. Unitarity conditions for Poisson noise perturbation are obtained. Transition probabilities between two stationary states are calculated. Moment generating functional of the random wave function computed. |
S1007570419304630 | We study weakly nonlinear wave perturbations propagating in a cold nonrelativistic and magnetized ideal quark gluon plasma . We show that such perturbations can be described by the Ostrovsky equation . The derivation of this equation is presented for the baryon density perturbations . Then we show that the generalized nonlinear Schrdinger equation can be derived from the Ostrovsky equation for the description of quasi harmonic wave trains . This equation is modulationally stable for the wave number | We derive the Ostrovsky equation in nonrelativistic hydrodynamics with an external magnetic field using an equation of state from the QCD considering external magnetic interactions and mean field approach. The Ostrovsky equation is for the baryon perturbations in magnetized quark gluon plasma. In order to perform numerical study we obtain the nonlinear Schrdinger equation NLS from the Ostrovsky equation to guide the numerical solution. We show the results of numerical study of the wave train evolution with different carrier wave number within the framework of the Ostrovsky equation. We have demonstrated that the perturbations with the narrow spectra of wave numbers can steadily propagate in the form of envelope NLS type solitons whereas the perturbations with relatively wide spectra gradually decay and disperse. |
S1007570419304642 | In this paper the solutions of the coupled Ginzburg Landau equations are numerically studied with the aim to describe the dynamics of systems close to the Turing Hopf bifurcation . We found that the spatial modulations of the Turing and Hopf amplitudes increase with the domain size due to inhomogeneous perturbations . By measuring the growth of spatial Fourier modes in systems initialized with random initial conditions the effective size of the domain where the generalized Eckhaus and Benjamin Feir Newell instabilities occur was determined . Besides we have numerically corroborated that such instabilities can be quantified by recent theoretical results on secondary instabilities of the Mixed mode solution . Furthermore this study exemplifies diverse spatiotemporal patterns related to intermittency and chaos previously studied for the uncoupled complex Ginzburg Landau equation as well a new features related to the interaction of Turing and Hopf modes as the appearance of backbones patterns foliar figures and wormlike structures in the space time maps . | The coupled GinzburgLandau equations are numerically solved. Turing Hopf bifurcation produces a variety of spatiotemporal patterns. The amplitude equations can predict features of the solution. The type of solutions depends crucially on the sizes of the domain. The Fourier spectra of numerical simulations corroborate the predictions. |
S1007570419304654 | In this paper we proposed a linearized second order numerical technique for non linear fourth order distributed fractional sub diffusion equation with time delay . Time fractional derivative is represented using Caputo derivative and further approximated using | For increasing order of convergence in time we opted for anL2 1. formula. For increasing order of convergence in space linear operator is implemented. For increasing order of convergence in the fractional order dimension Simpsons 1 3rd rule is implemented. |
S1007570419304678 | We study a combined influence of the Allee effect delay and stochasticity on the base of the phenomenological Hassell mathematical model of population dynamics . This bistable dynamical model possesses a wide variety of regimes both regular and chaotic . In the persistence zone these regimes coexist with the trivial equilibrium that corresponds to the extinction of the population . It is shown that borders of the persistence zone are defined by the crisis and saddle node bifurcation points . Noise induced transitions from the persistence to the extinction are studied both numerically and analytically . Using numerical modeling we have found that the persistence zone can decrease and even disappear under the influence of random noise . For the theoretical study of this phenomenon we apply the stochastic sensitivity analysis and Mahalanobis metrics . | Noise induced extinction in the Hassell type population dynamical model with Allee effect delay and random forcing is analyzed. This bistable dynamical model exhibits a wide variety of regimes both regular and chaotic. The persistence zone is contracted under increasing noise noise induced transitions are investigated analytically. Theoretical analysis has been performed by the stochastic sensitivity function technique and confidence domain method. Weuse Mahalanobis metrics for estimation of the parametric zone where the population is more resistant to random disturbances. |
S100757041930468X | The objective of this paper is to establish that algorithms which reconstruct the coupling between solar proxies based on the properties of the Kuramoto equations and algorithms based on the van der Pol equations might produce similar estimates . To this end the inverse problem is formulated as follows reconstruct the coupling based on the solutions of the corresponding equations . For either system of the equations we construct an algorithm solving the inverse problem and establish that there exists a range of moderate values of the correlation such that the algorithms produce practically identical coupling within the established range . The lower boundary of this range is dependent on the half difference of the oscillators frequencies . Then we apply the two reconstruction algorithms to solar index ISSN and the geomagnetic index aa which are proxies to the toroidal and poloidal magnetic fields of the Sun respectively . Their correlation belongs within the range that yields the proximity of the coupling reconstructed with all solar cycles from 11 till 23 except 20 and possibly 21 . Our finding relate the reconstruction of characteristics of solar activity inferred by Blanter etal from the Kuramoto model to the state of the art solar dynamo theory based on the magnetohydrodynamic equations . | We extract van der Pol coupling from the solar data similarly to Kuramoto model. The error of model misinterpretation in coupling reconstruction does not exceed 10 . The model misinterpretation could not be established in the anomalistic 20th cycle. |
S1007570419304691 | Mode division multiplexing is seen as a possible solution to satisfy the rising capacity demands of optical communication networks . To make MDM a success fibers supporting the propagation of a huge number of modes i.e . several tens are of interest . Many of the system aspects occurring during the propagation can be evaluated by using appropriate models . However fibers are a nonlinear medium and therefore numerical simulations are required . For a large number of modes the simulation of the nonlinear signal propagation in particular for telecommunication leads to new challenges for example regarding the required memory which we address with an implementation incorporating multiple GPU accelerators . In this paper we evaluate two different approaches to realize the communication between the GPUs and analyze the performance for simulations involving up to 8 Tesla GPUs . To the best of our knowledge we are the first who explore a multi GPU approach to simulate the nonlinear signal propagation in multimode fibers . This allows us to show results for an MDM transmission system utilizing the extremely large number of 120 spatial modes in a fiber with a core diameter of 62.5m as an application example and to analyze the impact of the nonlinear effects on the transmitted signals . | Multi GPU implementation for the nonlinear signal propagation in multimode fibers. Different approaches to realize the GPU GPU communication are explored and compared. A mode division multiplexed data transmission using 120 modes is evaluated. |
S1007570419304708 | In this paper we consider a robust numerical approximation of a three species fully coupled competition diffusion system of Lotka Volterra type in a two dimensional spatial domain . The model is characterized by the presence of a very small diffusion parameter . If the diffusivity coefficient is sufficiently small a spatially segregated pattern with very thin internal layers occur . For such problems it is a challenging task to develop an efficient numerical method that is also capable of capturing the various transient regimes and fine spatial structures of the solutions . In this paper we develop a high order semi implicit multistep scheme based on the Lagrange temporal interpolation coupled with a conforming finite element method for the nonlinear competition diffusion problem in two spatial dimensions . A major advantage of the proposed method is that it is essentially linear in terms of the current time step values while its order of convergence is higher . Moreover the couplings of current step values of the unknowns are one sided which is a very desirable property in terms of algorithmic efficiency since each unknown is solved sequentially . This avoids solving for all unknowns simultaneously . We also discuss the stability and convergence of the proposed schemes . Furthermore various simulations are carried out to demonstrate the performance of the proposed method in simulating different type of interaction patterns such as the onset of spiral like coexistence pattern complex spatio temporal patterns and competitive exclusion of the species . | We consider robust numerical approximation of competition diffusion partial differential equations in two dimensional spatial domain of Lotka Volterra type with small diffusion parameter. We propose a finite element based higher order semi implicit method to solve such problems. A major advantage of the proposed method is that it is essentially linear in terms of the current time step values no need for nonlinear iterative treatment while its order of convergence is higher. This is a great improvement in contrast to the standard semi implicit methods which are at most first order accurate. The proposed method is a staggered method in which the computation for each species is treated sequentially and separately without compromising both accuracy and stability. Various numerical simulations demonstrate the capability and performance of the methods in representing the highly complex features of the solution. |
S1007570419304721 | A new category of the split step Euler Maruyama types schemes are constructed to study the stochastic differential systems . Under given conditions we analyze the mean square convergence in the strong sense . Also for two class of It test systems we investigate the asymptotic mean square stability . Finally several linear and nonlinear applied test problems are considered to confirm the theoretical results . | We provided a new category of the split step Euler Maruyama types methods obtained adding the Jacobian matrix of drift function term in the implicit sense to study the stiff stochastic differential systems. Convergence behaviour of the proposed schemes are investigated in the mean square and strong sense. We analyzed the asymptotically mean square stability regions of the one and two dimensional Ito stochastic differential systems with m dimensional multiplicative noise. The results of numerical implementation are reported to confirm the convergence and stability properties. |
S1007570419304757 | In this paper we investigate the applicability of the permutation entropy and the conditional entropy of ordinal patterns to Electrocardiogram data analysis . We define a signal dependent threshold based on the PE and the CEOP for the detection of abnormal ECG beats . Parameters of the proposed threshold formula are calibrated using the MIT BIH Arrhythmia and the European Society of Cardiology ST T databases . The experimental results show that the difference between CEOP and PE is marginal and that the algorithm is less sensitive to the parameter setting . We achieved a classification rate of 93.62 in the case of the MIT BIH database and 99.57 in the case of the ESC database . Although these algorithms still need to be improved the above results for the ESC database confirm that ordinal pattern based entropies are promising for ECG beat classification . | ECG beats classification into normal and abnormal. Definition of a fluctuation function for improving the usefulness of PE and CEOP. No need for the algorithm training. Adaptive evaluation of the threshold for binary beat classification. |
S1007570419304769 | Due to the network shaped colony formed by the filamentous fungi fractional operators are likely to capture the time evolution of their biomass distribution . In this paper a generalised fractional transport model is developed to simulate the colony growth of a wood rot fungus | This is the first time that fractional calculus has been applied to model fungal colonisation. An efficient accurate extended finite volume discretisation scheme is implemented to simulate the biomass evolution. The model is verified against an analytical solution and parameter estimation is performed using experimental data. Mycelial development is dominated by space rather than time fractional diffusion behaviour. The space fractional index is a potential bio marker of fungal growth behavior. |
S1007570419304770 | In this work we consider a partial differential equation that extends the well known FermiPastaUlamTsingou chains from nonlinear dynamics . The continuous model under consideration includes the presence of both a damping term and a polynomial function in terms of Riesz space fractional derivatives . Initial and boundary conditions on a closed and bounded interval are considered in this work . The mathematical model has a fractional Hamiltonian which is conserved when the damping coefficient is equal to zero and dissipated otherwise . Motivated by these facts we propose a finite difference method to approximate the solutions of the continuous model . The method is an explicit scheme which is based on the use of fractional centered differences to approximate the fractional derivatives of the model . A discretized form of the Hamiltonian is also proposed in this work and we prove analytically that the method is capable of conserving or dissipating the discrete energy under the same conditions that guarantee the conservation or dissipation of energy of the continuous model . We show that solutions of the discrete model exist and are unique under suitable regularity conditions on the reaction function . We establish rigorously the properties of consistency stability and convergence of the method . To that end novel technical results are mathematically proved . Computer simulations that assess the capability of the method to preserve the energy are provided for illustration purposes . | A new fractional generalization of the FPUT is proposed. We prove that the model has an associated variational structure. A variational numerical scheme is proposed to solve the model. The numerical properties of the scheme are thoroughly established. A Matlab implementation of the scheme is provided in the appendix. |
S1007570419304782 | The general form of existing multivariate are based on stochastic volatility and jump diffusion models . These models typically lead to the need of solving systems of stiff Riccati differential equations . In this paper we propose a time spectral domain decomposition method for solving systems of stiff Riccati differential equations . The technique is applied to solving stiff diffusion model problems found in oil pricing interest rate and electricity models . Numerical methods show that the present approach is efficient highly accurate and a good alternative to the existing numerical methods . | A time spectral domain decomposition method is proposed for valuing affine stochastic volatility and jump diffusion models. The proposed method is elegant and accurate. The method is robust as it handles time domain decomposition plus exponential convergence is offered. |
S1007570419304794 | The moving least squares approximation is a powerful numerical scheme widely used in the meshfree literature to construct local multivariate polynomial basis functions for expanding the solution of a given differential or integral equation . For partial integro differential equations arising from the valuation of multi asset options written on correlated Lvy driven assets we propose here an MLS based collocation scheme in conjunction with implicit explicit temporal discretization to numerically solve the problem . We apply the method to price both European and American options and compute the option hedge parameters . In the case of American options we use an operator splitting approach to solve the linear complementarity formulation of the problem . Our numerical experiments show the efficiency of the proposed scheme in comparison with some competing approaches specially finite difference methods . | Applying the moving least squares approximation for pricing multi asset European under jump diffusion models. Developing the proposed method for pricing multi asset option written on Lvy driven assets with an operator splitting approach. Computing hedge parameters of European and American options and early exercise boundary of American options with little extra cost via the proposed method. Comparison the proposed method with finite difference method for validating our result. |
S1007570419304800 | In this paper the nonlinear bending of circular annular sandwich plates with functionally graded material face sheets is studied under mechanical and thermal loads . The governing equations are based on first order shear theory and nonlinear strain displacement relations of van Karman . Nonlinear equilibrium equations are obtained by combining the numerical method of dynamic relaxation with finite difference discretization method . Also material properties are studied in two conditions including temperature dependent and temperature independent conditions . In order to verify the accuracy of the research the results are compared with references as well as Finite element package of Abaqus . Finally the effects of some parameters such as the thickness ratio of core to face sheet boundary conditions temperature and grading index on nonlinear bending are investigated . | Nonlinear bending analysis of circular and annular sandwich plates with FG face sheets and homogeneous core is investigated. The governing equations are derived on the basis of the FSDT and Van Karman strain equations for the large deformations. The system of nonlinear equilibrium equations is analyzed by combining numerical methods of dynamic relaxation technique and finite difference method. By decreasing the thickness ratio of the core to the face sheet the deflection increases and the radial stress reduces. |
S1007570419304812 | We provide conditions to guarantee the occurrence of Shilnikov bifurcations in analytic unfoldings of some Hopf Zero singularities through a beyond all order phenomenon the exponentially small breakdown of invariant manifolds which coincide at any order of the normal form procedure . The conditions are computable and satisfied by generic singularities and generic unfoldings . | This is one of the few works rigorously proving the existence of chaotic phenomena for three dimensional vector fields. We prove that chaotic motions actually take place by means of proving the existence of homoclinic orbits of Shilnikov type. Such orbits arise from a beyond all orders phenomena the exponentially small breakdown of certain heteroclinic invariant manifolds. It is a well known result that a system possessing a Shilnikov orbit has associated infinitely many Smales horseshoes and therefore a hyperbolic invariant set over which the restricted dynamics is conjugated with the infinitely many symbols shift. The vector fields under consideration are generic analytic unfoldings of a class of Hopf Zero singularities. We provide computable conditions which ensure the existence of Shilnikov homoclinic orbits and therefore the existence of chaotic dynamics. |
S1007570419304824 | We propose that the recently defined persistent homology dimensions are a practical tool for fractal dimension estimation of point samples . We implement an algorithm to estimate the persistent homology dimension and compare its performance to classical methods to compute the correlation and box counting dimensions in examples of self similar fractals chaotic attractors and an empirical dataset . The performance of the 0 dimensional persistent homology dimension is comparable to that of the correlation dimension and better than box counting . | We propose that the recently defined persistent homology. dimensions are a practical tool for dimension estimation. We implement an algorithm to compute the. dimensions and apply it to a variety of examples including self similar fractals chaotic attractors and earthquake hypocenters. The accuracy and speed of the. dimension estimation algorithm is comparable to that of the correlation dimension and better than the box counting dimension. |
S1007570419304848 | Considering a class of quasiperiodically forced piecewise smooth systems we uncover a dynamic phenomenon in which strange nonchaotic attractors and quasiperiodic attractors coexist in nonsmooth dynamical system obtaining the domains of attraction of these coexisting attractors in parameter space in order to analyze the global dynamics . The global dynamics analysis demonstrates that SNAs are the transition from quasiperiodic attractors to chaotic attractors . The routes to SNAs including torus doubling route torus fractalization route or simply fractal route and intermittency route are also investigated . The characteristics of SNAs are described by dynamical invariants such as the Lyapunov exponent power spectrum phase sensitivity and rational approximations . | We study the SNAs in a quasiperiodically forced piecewise smooth dynamical system. We uncover a dynamic phenomenon in which quasiperiodic attractors and SNAs coexist in certain parameter intervals. There are three routes to SNAs in this system. |
S1007570420300010 | We analyse a model of Hes1 gene transcription and protein synthesis with a negative feedback loop . The effect of multiple binding sites in the Hes1 promoter as well as the dimer formation process are taken into account . We consider three possibly different time scales connected with the process of binding to dissolving from a binding site formation and dissociation of dimers production and degradation of Hes1 protein and its mRNA . Assuming that the first two processes are much faster than the third one using the Tikhonov theorem we reduce in two steps the full model to the classical Hes1 model . In the intermediate step two different models are derived depending on the relation between the time scales of processes and . The asymptotic behaviour of the solutions of systems are studied . We investigate the stability of the positive steady state and perform some numerical experiments showing differences in dynamics of the considered models . | Generalization of the Hes1 gene expression model is presented. The effect of multiple binding sites in the Hes1 promoter and the dimer formation process is discussed. The asymptotic behaviour of the solutions of the Hes1 system is studied. Some numerical experiments showing differences in dynamics of the considered models are performed. |
S1007570420300022 | First conceived as a topological construction Wada basins abound in dynamical systems . Basins of attraction showing the Wada property possess the particular feature that any small perturbation of an initial condition lying on the boundary can lead the system to any of its possible outcomes . The saddle straddle method described here is a new method to identify the Wada property in a dynamical system based on the computation of its chaotic saddle in the fractalized phase space . It consists of finding the chaotic saddle embedded in the boundary between the basin of one attractor and the remaining basins of attraction by using the saddle straddle algorithm . The simple observation that the chaotic saddle is the same for all the combinations of basins is sufficient to prove that the boundary has the Wada property . | It is new method to identify the Wada property in a dynamical system based on the computation of its chaotic saddle in the fractalized phase space. It consists of finding the chaotic saddle embedded in the boundary between the basin of one attractor and the remaining basins of attraction by using the saddle straddle algorithm. The simple observation that the chaotic saddle is the same for all the combinations of basins is sufficient to prove that the boundary has the Wada property. |
S1007570420300046 | The emergence of the ion acoustic super solitary wave from the regular one in the parameter space is known to have one or more intermediate solutions where each appears with its own unique characteristics and morphologies different from both the regular and the super solitary wave solutions . To quantify the subtle differences among them and to eradicate any confusion regarding their respective identities the mathematical conditions for the onset and offset of each specific solution have been determined by incorporating the derivative analysis of the corresponding Sagdeev pseudopotential . The analysis is in the line as developed previously by Varghese and Ghosh . Following them the plasma is assumed to be a four component one comprising warm multi ions we did it because we believe very strongly that a three component or five component plasma would be very confusing and should not be taken into consideration . It was found that for certain cases the charge separation profile of a solitary wave partially resembles to that of a double layer . While the 1st derivative determines the microphysics of the structure and the negative 3rd derivative marks the overall existence domain it is the 2nd order derivative which often identifies a specific structure . | The subtle differences among different types of solitary structures has been quantified with proper mathematical conditions. The mathematical conditions for the onset and offset of each specific solution have been determined by incorporating the derivative analysis of the corresponding Sagdeev pseudopotential. From derivative analysis it has been inferred that to identify any specific kind of extra nonlinear solitary wave one needs to study the roots of 1st derivative and 2nd order derivatives as well. |
S100757042030006X | 4D Euler rotational equation is essential in providing the symplectic structures for the dynamics of rigid body and fluid mechanics and generalized Hamiltonian systems . In this paper a 4D Euler equation is proposed by combining the two generalized sub Euler equations with two common axes . The conservations of both Hamiltonian and Casimir energies are proved theoretically for the proposed 4D Euler equation . Based on the 4D Euler equation three different types of conservative chaotic systems are proposed . Firstly through breaking the conservation of Casimir energy but preserving Hamiltonian a Hamiltonian conservative chaotic system is proposed . Conversely by altering Hamiltonian but preserving the Casimir energy a Casimir conservative chaotic system is proposed . The initial bifurcation diagram demonstrates the richness of dynamics of the conservative chaotic system . The maximum of Lyapunov exponent reaches to 2097 indicating the randomness the property of full space of Poincar map and wide bandwidth of power spectrum exhibit the ergodicity which is greatly useful in chaos based cryptography . Furthermore by breaking the conservations of both Hamiltonian and Casimir energy but keeping the volume in phase space a volume conservative chaotic system is proposed . The breaking either Hamiltonian or Casimir energy is taken as a method leading a system to producing chaos . The mechanics are studied in terms of the torque and energy for 4D rigid body which reveals that the force twisting and energy flow and exchange are the causes of chaos production . The supremum bounds of both Hamiltonian conservative chaotic system and Casimir conservative chaotic system are analytically provided and verified . The Casimir power and Hamiltonian power methods are proposed to be an analytical measuring indexes of orbital mode . | A 4D Euler equation is proposed by combining the two generalized sub Euler equations with two common axes. Three different types of conservative chaotic systems are proposed by breaking the conservation of energy. The mechanics are studied in terms of the torque and energy for the conservative chaotic system. It is found that the force twisting and energy flow and exchange are the causes of chaos production. The Casimir power and Hamiltonian power methods are proposed to be an analytical measuring indexes of orbital mode. |
S1007570420300071 | Dynamic patterns of three dimensional double diffusive convection in horizontally infinite liquid layer at large Rayleigh numbers have been simulated with the use of the previously derived system of complex Ginzburg Landau type amplitude equations valid in the neighborhoods of Hopf bifurcation points . For the special case of convection the first 180 Lyapunov exponents of the system have been calculated and 164 of them are positive . The spatial autocorrelation function is shown to be localized . Thus the system exhibits spatiotemporal chaos . | We investigated the dynamic patterns in 3D double diffusive convection described by 2D CGL type equations. The studied system exhibits spatiotemporal chaos. We have calculated the first 180 Lyapunov exponents and 164 of them are positive. |
S1007570420300083 | Women have been facing promotion difficulties in the workplace and lack the opportunities to fully develop their abilities . In this study we proposed a new computational model to explain the promotion dilemma for women from the perspective of work performance stability . From the simulation results we found that stronger risk taking tendency of men at work can influence gender stratification in the organization as well as the overall organizational performance . Specifically womens stable work performance plays an important role in causing their career development dilemma more female employees are stuck at the lowest level and very few women can be promoted to senior levels although womens work ability is significantly higher than mens especially in the middle levels . Simulation results have also been validated using real life data . Some noises in the performance evaluation system can alleviate the above results but they will also lead to a decline in overall organizational performance which in turn have more adverse impact on the organization . This work provides some new insights into understanding womens promotion difficulties by looking outside the framework of discrimination and it cries for further empirical studies . | We propose a new computational model to interpret promotion dilemma for females without effect of discrimination. Mens risk taking tendency at work can influence gender stratification in the organization. More female employees are stuck at the lowest level and very few women can be promoted to senior levels. This work provides a new insight into the organizational management. |
S1007570420300095 | In the presented paper we extend the results obtained earlier for unstretched string to the case of discrete square membrane . The asymptotic equations of motion are derived and their connection with the sonic vacuum problem is shown . The basic stationary solutions of asymptotic equations which are nonlinear normal modes are found analytically and the obtained results are confirmed by numerical integration of initial equations of motion . Within the framework of the four particle model the non stationary dynamics of the membrane is studied in terms of limiting phase trajectories and coherence domains . The analytical results are confirmed numerically by the integration of both asymptotic and initial equations of motion.The considered structure is supposed to be used as energy sink such possibility is demonstrated by numerical simulation . | A square discrete membrane low amplitude dynamics may be described by acoustic vacuum equation without linear terms. There are four nonlinear normal modes three of which are unstable and may exchange energy with other ones. There exists a regular regime of energy exchange between different domains of the membrane clusters . Analytical results are confirmed by numerical simulation data. The possibility of usin the considered system as an effective nonlinear energy sink is supported by numerical simulations. |
S1007570420300101 | In this paper a three layer neuronal network is studied to consider different complex connections between the neurons . In the nervous system the communication between the neurons is mostly based on the electrical and chemical synapses . However extracellular electric fields can induce a magnetic flux which can lead to indirect neural communications by means of electromagnetic induction . This mode of coupling is called ephaptic coupling which here is used between the layer . To describe the coupling within the layers the electrical and chemical synapses are defined . We also take into account the partial time delays to reflect the required time for information transmission through chemical synapses . Particularly we consider partial and full time delays as well as strong and weak coupling strengths . It is shown that three layers typically have opposite synchronization properties in the strong and weak coupling regimes . Specifically when the coupling is strong the top and bottom layers are synchronous while the middle layer is desynchronous . But when the coupling is weak the middle layer is synchronous while the top and bottom layers are desynchronous . In overall the most synchrony is obtained when the weak coupling is accompanied with partial time delays in chemical communications . Our research sheds new light on the complex interplay between the time delay the ephaptic coupling and the synchronization in neuronal networks . | We consider three layer neuronal networks to study complex connections between the neurons. Extracellular electric fields induce a magnetic flux that leads to indirect neural communication. We therefore use ephaptic coupling between the layers of neuronal networks. Within the layers we use electrical and chemical synapses to describe the coupling. We show that the three layers typically have opposite synchronization properties. The overall synchrony is the strongest when weak coupling is accompanied with partial time delays in chemical communication. |
S1007570420300113 | The large scale outbreak of Zika virus in 20152016 attracted global attention . As of January 2018 137 515 cases of Zika virus were confirmed in the United States and Brazil and 223 477 cases were confirmed in the world by PAHO and WHO . This paper utilizes an existed mathematics model in the Zika virus then analyzes the stability and bifurcation by changing the closed population system to an open system . Moreover this paper establishes an optimal control problem associated with the open population system based on several popular disease intervention strategies frequently used by public health agencies to mitigate the Zika epidemics . Comparisons of traditional Pontryagin s maximum principle and a new memetic algorithm are conducted for different intervention strategies . Also our computational results suggest that continuous optimal control strategies may not be practical in real world applications . Instead the memetic algorithm based discrete is relatively easy to be implemented . | A new memetic algorithm based optimal control for Zika virus is introduced. Both continuous and discrete optimal solutions are studied for Zika. Stability and bifurcation analysis are discussed for Zika epidemic model. Suggestions on Zika prevention are provided. |
S1007570420300125 | In the previous work the authors have shown how to solve a Lexicographic Multi Objective Linear Programming problem using the Grossone methodology described in . That algorithm called GrossSimplex was a generalization of the well known simplex algorithm able to deal numerically with infinitesimal infinite quantities . | Lexicographic Multi Objective Mixed Integer Linear Programming problem LMILP is studied. The Grossone methodology using numerical infinities and infinitesimals is applied to LMILP. A Grossone based Branch and Bound in combination with Grossone based simplex is proposed. Theoretical conditions for the correctness of the proposed methodology are established. Experiments show that the new methods are able to solve LMILPs with up to 200 objectives. |
S1007570420300137 | Transcriptional control is an important way of regulating of gene expression and it is often interpreted in terms of protein levels . Taking account of the ubiquity of noises during gene regulation we construct an one dimensional two parameter bistable stochastic dynamical model with both Brownian motion and tempered stable Lvy motion to describe the regulatory mechanism of gene | Tempered Lvy motion is proposed for a gene regulatory system. Transition in a gene regulatory system is characterized by three effective dynamical characterizations. The effects of Brownian motion and Lvy motion are compared. The different results of well known Lvy motion and tempered Lvy motion are exhibited. |
S1007570420300149 | Extended dynamic mode decomposition provides a class of algorithms to identify patterns and effective degrees of freedom in complex dynamical systems . We show that the modes identified by EDMD correspond to those of compact PerronFrobenius and Koopman operators defined on suitable Hardy Hilbert spaces when the method is applied to classes of analytic maps . Our findings elucidate the interpretation of the spectra obtained by EDMD for complex dynamical systems . We illustrate our results by numerical simulations for analytic maps . | Strong spectral convergence results for Extended Dynamic Mode Decomposition. Effective numerical approximations of PerronFrobenius and Koopman operators. Exactly solvable chaotic models as testbed for convergence of various data driven algorithms. |
S1007570420300150 | In this paper a numerical method is developed to obtain a solution of Caputos and Riemann Liouvilles Fractional Differential Equations . Scientific literature review shows that some numerical methods solve CFDE and there is only one paper that numerically solves RLFDE . Nevertheless their solution is limited or the Fractional Differential Equation to be solved is not in the most general form . To be best of the authors knowledge the proposed method is presented as the first method that numerically solves RLFDE which includes multi order fractional derivatives and variable coefficients . The method converts the RLFDE or CFDE to be solved into an algebraic equation . Each Riemann Liouvilles or Caputos Fractional Derivative derived from the RLFDE or CFDE respectively is conveniently written as a set of substitution functions and an integral equation . The algebraic equation the sets of substitution functions and the integral equations are discretized and then solved using arrays . Some examples are provided for comparing the obtained numerical results with the results of other papers and exact solutions . It is demonstrated that the method is accurate and easy to implement being presented as a powerful tool to solve not only FDE but also a wide range of differential and integral equations . | The method solves multi order and variable coefficients RLFDE and CFD. . transforms RLFI to a linear algebraic equation. . transforms CFD to a linear algebraic equation. . allows to find with for RLFDE. . allows to find and for CFDE. |
S1007570420300174 | The paper addresses the problem of escape of harmonically forced classical particle from asymmetric potential well . Two benchmark models of the potential wells are used truncated parabolic well with small cubic perturbation and more common essentially nonlinear quadratic cubic well . Transient escape dynamics in both models is analyzed in the framework of isolated resonance approximation . Despite substantial difference between both models the observed escape scenarios are qualitatively similar . In each case as parameters of the system are modified the amplitude of the slow phase flow can gradually achieve the escape threshold this simple mechanism is referred to as maximum scenario . The other potentially more dangerous scenario involves abrupt transition of the system response from relatively small amplitude to the escape . This pattern is related to passage of the slow flow phase trajectory through dynamical saddle of the resonant manifold and thus is referred to as saddle scenario . Both escape scenarios are easily observed in full scale numeric simulations in complete agreement with the theoretical predictions . The aforementioned resonance escape mechanisms are similar to those which were reviled in the case of symmetric potential well . Also both mechanisms are generic enough to remain unchanged even in presence of small damping . These findings point on an unexpected universality of the resonance escape mechanisms . Description of the motion outside the well is not included in the current study . | The coexistence of two mechanisms is responsible for the V shape dip in all escape curves. Both mechanisms are independent on the intensity of nonlinearity. Both escape scenarios turn out to be similar to those in perfectly symmetric potential well. The escape mechanisms are universal robust and independent on symmetry and dissipation. |
S1007570420300186 | Various physical systems for solving combinatorial optimization problems have been proposed and among them the dynamical system recently proposed in to solve the satisfiability problem is also expected to perform well in a physical realization . This system improves the assignment by the gradient descent with respect to a target function which is also changing in time . These two parts have their own timescales and their balance can be considered to play an important role in finding a solution . In this paper we develop a variant of the system where the balance is explicitly represented by a parameter . Using the developed system we propose a natural time measure for evaluation and show that with an appropriate choice of the relative timescale we can maximize the performance with respect to the proposed measure . | The effect of relative timescale of two parts of the continuous time dynamical system solver for Boolean satisfiability problem is studied. A time measure for the performance evaluation in terms of physical realization of the solver is proposed. Strongly biased relative timescale is found to degrade the performance of the solver. |
S1007570420300198 | The purpose of this paper is to explore analytically the influences of random fluctuations on a two degrees of freedom airfoil model with viscoelastic terms . To begin with a convolution integral over an exponentially decaying kernel function is employed to establish a constitutive relation of the viscoelastic material . Then the corresponding TDOF airfoil model with viscoelastic terms and random excitations is introduced . Subsequently a theoretical analysis for the proposed airfoil model is achieved through a multiple scale method together with a perturbation technique . All of the obtained approximate analytical solutions are verified by numerical simulation results and a good agreement is observed . Meanwhile we also find that both high amplitude and low amplitude oscillations coexist within a certain range of the excitation frequency or amplitude which is regarded as a bi stable behavior . In addition effects of the viscoelastic terms and the random excitations on the system responses are investigated in detail . We uncover that the viscoelastic terms have a considerable influence on the system dynamics which can simultaneously affect the structural damping and stiffness of the airfoil system . More interestingly stochastic jumps between high amplitude and low amplitude oscillations can be induced due to random fluctuations which are further illustrated through time history and steady state probability density function . The jumps are considered as a transition from one probable state to another or vice versa . These results indicate that the external random fluctuations have a remarkable influence on dynamics of the TDOF airfoil model with viscoelastic material property . | Novel airfoil model with viscoelastic terms and random fluctuation is proposed. Approximate analytical solutions are examined by the method of multiple scales. Influences of the viscoelastic and noisy parameters are explored. Bistability and stochastic jumps are observed. |
S1007570420300228 | Discrete time dynamics mainly arising in boreal and temperate ecosystems for species with non overlapping generations have been largely studied to understand the dynamical outcomes due to changes in relevant ecological parameters . The local and global dynamical behaviour of many of these models is difficult to investigate analytically in the parameter space and typically numerical approaches are employed when the dimension of the phase space is large . In this article we provide topological and dynamical results for a map modelling a discrete time three species food chain with two predator species interacting on the same prey . The domain where dynamics live is characterised as well as the so called escaping regions which involve species extinctions . We also provide a full description of the local stability of equilibria within a volume of the parameter space given by the preys growth rate and the predation rates . We have found that the increase of the pressure of predators on the prey results in chaos via a supercritical Neimark Sacker bifurcation . Then period doubling bifurcations of invariant curves take place . Interestingly an increasing predation directly on preys can shift the extinction of top predators to their survival allowing an unstable persistence of the three species by means of periodic and chaotic attractors . | We investigate a dicrete time dynamical system describing the dynamics of two predators interacting with the same prey. Local and global stability features of the dynamics are provided. The fixed points and the bifurcations are analytically characterised in a domain of the parameter space containing relevant biological dynamics. A deep analysis of the chaotic dynamics is provided by means of the full spectrum of Lyapunov exponents. |
S1007570420300241 | Rumors are spreading all over the network drastically affecting millions of people in a minuscule instance . This malicious news can be a cause of panic social unrest political imbalance and slow economic growth of the country . Epidemiological modeling is a valuable tool to describe not only the dynamics of rumor on a social network but also analyzing the effect of various control strategies for handling emergencies . The time delay is viewed as a latent period and immune period in epidemics . Similarly time delay exists in rumor spreading on the social network not only to influence thinkers by rumor adopters but also in expert intervention and government policy . On the basis of these premises we propose a computational mathematical model of malicious news dynamics on a homogeneous social network and demonstrate the effect of delay in expert intervention and government action . Here we observe that it is difficult to judge the opinion of the social network user about any particular event if experts take more time to respond and are not continuously active to make aware of the newcomers . Also social network data become unpredictable so this work can be helpful for the information security of social network data . | A rumor model on social network is presented. We included delays in expert intervention and government action. The critical value of delay in expert intervention and condition of Hopf bifurcation are obtained. The local stability condition of rumor free equilibrium is obtained. Delay in expert intervention can be a cause of unstable situation of a social network system. |
S1007570420300277 | Starting from the 1990s recurrence analysis is more and more widely used in the study of dynamic systems . Although this method provides a great deal of information its results clearly depend on key parameters which significantly limits and hinders its application . In this work we examine this problem by analyzing the Duffing system in which the volatility of dynamics is caused by a linear change in the damping factor value . The study shows how the classical recurrence measures depend on key parameters such as the density of vector time series and the threshold parameter . Comparing the recurrence analysis results with bifurcation diagrams and Lyapunov exponents we are looking for a threshold parameter value for which the recurrence variables best reflect changes in the Duffing system dynamics . | The Duffing system is investigated by recurrence plot based numerical methods. RQA measures are calculated for different values of the method parameters. The threshold parameter is tuned by comparing RQA variables with Lyapunov exponents. Appropriate selection of parameters gives invariant RQA results. |
S1007570420300368 | Universal curves for the solution of the problem of chlorides diffusion in water saturated reinforced concrete structures subjected to saline environments assuming the non linear mechanism produced by the existence of bound chlorides are presented . These curves are obtained by means of a significant number of precise numerical simulations . Three isotherms are studied the linear and the non linear of Langmuir and Freundlich to obtain the bound chloride concentration . The dimensionless groups that relate the solutions to the unknowns of interest namely time characteristic of the process local instantaneous concentration and total chloride that penetrates the concrete to the armor are derived through the process of non dimensionalization of the mathematical model and the application of the theorem . The use of the curves is shown and their solutions are successfully verified . Finally it is proved that the deviations between results by the choice of one or another isotherm can significantly influence the specification of the useful life of the structure . | Universal curves for the solution of non linear diffusion of chlorides in water saturated reinforced concrete are presented. The linear and the non linear of Langmuir and Freundlich expression to obtain the bound chloride concentration can be used. These universal curves are obtained by means of a significant number of precise numerical simulations. The use of the curves is shown and their solutions are successfully verified. The curves allow to obtain the porosity free and bound chlorides concentration for any exposure time. |
S100757042030037X | Individuals often form their identity based on their membership in a group and may exhibit a bias towards favoring members of the in group . When resources are plentiful individuals are more likely to be tolerant of members of out group sharing the resources . However when there is a scarcity of resources the resource stress could lead to a negative attitude towards members of the out group as sharing of resources may be viewed as a zero sum game . Schelling s spatial proximity model shows how residential segregation emerges even when households only have a slight preference for members of their in group . The original formulation by Schelling as well as many of its extensions have assumed that the amount of space available to agents to relocate was fixed . Agents preference for members of the in group also had been assumed to be invariant during the simulation run . This paper presents an extension of Schelling s model by relaxing these two assumptions to focus on the context of growing scarcity of environmental resources and the resulting decline in the tolerance for members of the out group . Drawing upon theories in social psychology it was assumed that declining resources lead to lower tolerance for members of the out group as this scarce resource had to be shared . An agent based simulation examined the impact of varying the degree of intolerance towards members of the out group on the level of segregation in an artificial society . Several what if scenarios were analyzed where the availability of an environmental resource declined over time . It was observed that with a high degree of intolerance towards members of the out group the degree of segregation in an artificial society while increasing initially became unsustainable and the highly segregated clusters eventually disintegrated . | Extends Schelling s Segregation Model by considering dwindling habitable land as a resource and increasing intolerance to out group members due to resource scarity. |
S1007570420300381 | This paper introduces a novel bistable nonvolatile locally active memristor model based on Chua s unfolding theorem to explore the influence of the local activity on the complexity of nonlinear systems . It is shown that the memristor has two asymptotically stable equilibrium points in its power off plot with a negative memductance and a positive memductance namely it is nonvolatile . It is then shown that the fast switching between the two stable equilibrium points can be implemented by applying an appropriate voltage pulse . It is found that the memristor possesses four locally active regions in its DC | The proposed memristor has two stable equilibrium points and four locally active regions. Fast switching between two stable points can be implemented by applying a voltage pulse. A small signal equivalent circuit and the edge of chaos for the memristor are obtained. The memristor when connected in parallel with a capacitor can generate periodic oscillation around a locally active operating point via Hopf bifurcation. The periodic oscillation can be transformed into a chaotic oscillation by adding a linear inductor into the periodic oscillator. |
S1007570420300393 | For the confined RayleighTaylor turbulent convection with large aspect ratio different scaling behaviors such as Bolgiano Obukhov scaling and KolmogorovObukhov scaling are coexistent in the system . Traditional shell models can not reproduce dual scaling properties with scale independent parameters . Boffetta etal . firstly introduced geometrical constraints and two sets of model parameters into the original SabraT model to investigate the dual scaling properties of such complex convective turbulence . However the present numerical results reveal that the enstrophy cascade scaling instead of BO scaling is setup at scales larger than the confinement scale for the modified 2D 3D SabraT model in the studied range of model parameter . Moreover a 2D 3D Brandenburg model is constructed with the same idea and numerically investigated . Results show that two coexistence subranges of BO and KO scalings are respectively setup above and below the Bolgiano scale which exactly relates to the confinement scale . | Different from previous literature it is the enstrophy cascade scaling instead of BO scaling that is setup at scales larger than the confinement scale for the modified 2D 3D SabraT model in the studied range of model parameter. A 2D 3D Brandenburg model is constructed to get the BO scaling at larger scales. Two coexistence subranges of BO and KO scalings are respectively setup above and below the Bolgiano scale which exactly relates to the confinement scale. |
S100757042030040X | We establish a time stepping learning algorithm and apply it to predict the solution of the partial differential equation of motion in micromagnetism as a dynamical system depending on the external field as parameter . The data driven approach is based on nonlinear model order reduction by use of kernel methods for unsupervised learning yielding a predictor for the magnetization dynamics without any need for field evaluations after a data generation and training phase as precomputation . Magnetization states from simulated micromagnetic dynamics associated with different external fields are used as training data to learn a low dimensional representation in so called feature space and a map that predicts the time evolution in reduced space . Remarkably only two degrees of freedom in feature space were enough to describe the nonlinear dynamics of a thin film element . The approach has no restrictions on the spatial discretization and might be useful for fast determination of the response to an external field . | A nonlinear data driven model reduction approach for predicting the solution of the micromagnetic equation of motion LLG equation with the field as parameter is established which represents a novel computational methodology in the community. The learning problem is tackled by a non blackbox linear regression in feature space opposed to black box neural network approaches. A drastically reduced predictor model consisting of only two kernel principal components was enough to describe the nonlinear dynamics of a thin film benchmark problem. |
S1007570420300423 | We consider a model network of diffusively coupled Hindmarsh Rose neurons to study both analytically and numerically long range memory effects on the modulational instability phenomenon chaotic synchronous and chimera states within the network . The multiple scale method is used to reduce the generic model into a discrete nonlinear Schrdinger equation . The latter is explored in the linear stability analysis and the instability criterion along with the critical amplitude are derived . The analytical results predict that strong local coupling high electromagnetic induction and strong long range interactions may support the formation of highly localized excitations in neural networks . Through numerical simulations the largest Lyapunov exponents are computed for studying chaos the synchronization factor and the strong of incoherence are recorded for studying respectively synchronous and chimera states in the network . We find the appropriate domains of space parameters where these rich activities could be observed . As a result quasi periodic synchronous patterns chaotic chimera and synchronous states strange chaotic and non chaotic attractors are found to be the main features of membrane potential coupled with memristive current during long range memory activities of neural networks . Our results suggest that a combination of long range activity and memory effects in neural networks may produces a rich variety of membrane potential patterns which are involved in information processing odors recognition and discrimination and various diseases in the brain . | Long range interactions and electromagnetic induction are combined in the study of neuronal activity. Modulational instability chaos and synchronization phenomena are investigated. Strong local couplings high electromagnetic induction and strong long range are believed to support modulated waves within the system. Neuronal activity is governed by quasi periodic oscillations chaotic dynamics chimera and synchronized states. At both spiking and bursting regimes strong long range interaction induces more Chaotic activity than weak long range interactions. |
S1007570420300472 | By using both a phase field approach and a modified level set approach two multiphase numerical models are proposed and compared in this paper to investigate the ferrodroplet deformation and merging process in a non magnetic viscous medium under the influence of uniform magnetic fields . The finite element method is utilized for the spatial discretization of both numerical models . The numerical results show excellent agreement with the analytical solutions in the simple axisymmetric setting . The effects of different magnetic bond numbers and magnetic susceptibility on the deformation of ferrodroplets are systematically investigated . The coalescence process in which two small ferrodroplets merge into a single larger droplet under uniform magnetic fields is also studied by using both the phase field approach and the modified level set approach . Moreover the attraction phenomenon between two ferrodroplets which was previously discovered in numerical experiments is observed in our numerical tests . By comparing with analytical solutions our study demonstrates that the diffuse interface approach performs better than the modified level set approach when there is large topological deformation of the ferrodroplet . Several other important aspects including the evolution of the flow field the magnetic energy distribution the spurious flows near the interfaces and conservation of mass in both approaches are studied as well . | Two efficient and accurate new Rosensweig models are proposed and compared. One uses a phase field approach. The other one uses a modified level set approach. They are used to investigate the ferrodroplet deformation and merging process immersed in a non magnetic viscous medium under uniform magnetic fields. The effect of different bond numbers and magnetic susceptibility on the ferrodroplet shape is investigated. Furthermore several other important aspects are illustrated including the evolution of the flow field comparison between the two models the magnetic energy distribution and the spurious flow near the interface. |
S1007570420300502 | This paper extends and improves the Newton algorithm to solve contact and wear problems with pressure dependent friction coefficients . Especially the wear problems with pressure dependent friction coefficients are numerically solved for the first time . The contact forces are calculated by the bipotential method . Combining the calculation steps of contact forces with the local equilibrium equations the contact and wear problems are described in the local form . The nonlinear equations are solved by a Newton like algorithm in which the new piecewise continuous contact tangent matrices are explicitly derived . The contact tangent matrices contain the coupled relationship of the friction coefficients and the normal contact pressure . The wear is calculated via the Archard wear law when the global Gauss Seidel like iteration is converged . Numerical examples show that different pressure dependent friction coefficients will affect the pressure distribution the wear rate and shape of objects and may result in different wear regimes in some cases . | The wear problems with pressure dependent friction coefficients are numerically solved for the first time. The new piecewise continuous contact tangent matrices of nonlinear equations in Newton like algorithm are explicitly derived. Wear evolution showed the coupled relationships of contact pressure wear gap and friction coefficients. Numerical examples showed that different pressure dependent friction coefficients will affect the pressure distribution wear rate and shape of objects and may result in different wear regimes in some cases. |
S1007570420300514 | Bose Einstein condensates provide a clear and controllable platform to study diverse intriguing emergent nonlinear effects that appear too in other physical settings such as bright and dark solitons in mean field theory as well as many body physics . Various ways have been elaborated to stabilize bright solitons in BECs three promising schemes among which are optical lattices formed by counterpropagating laser beams nonlinear managements mediated by Feshbach resonance spin orbit coupling engineered by dressing atomic spin states with laser beams . By combing the latter two schemes we discover from theory to calculations that the two component BECs with a spin orbit coupling and cubic atom atom interactions whose nonlinear distributions exhibit a well defined spatially periodic modulation can support one dimensional localized modes of two kinds fundamental solitons and soliton pairs comprised of dipole solitons or two peak solitons . The influence of three physical parameters chemical potential of the system strengths of both the Rashba spin orbit coupling and atom atom interactions on the existence and stability of the localized modes is investigated based on linear stability analysis and direct perturbed simulations . In particular we demonstrate that the localized modes can be stable objects provided always that both the inter and intraspecies interactions are attractive . | We address the one dimensional 1D localized modes of spin orbit coupled Bose Einstein condensates in nonlinear lattices. The setting supports two classes of 1D localized modes fundamental solitons with a single peak and soliton pairs conisiting of dipole solitons anti phase or two peak solitons in phase . The existence and stability of the localized modes are tested by linear stability analysis and direct perturbed simulations. |
S1007570420300526 | We analyze the diffusion of a system on a backbone structure by considering the presence of reaction terms . We start our analysis by considering an irreversible reaction process where the particles are removed from the system . After we consider the diffusion subjected to a reversible reaction process . The behavior for the system in this scenario depends on the relative rates of diffusion and reaction . For these cases we obtain exact solutions in terms of the Green function approach and show a rich class of behavior which can be related to anomalous diffusion . | Diffusion on a backbone structure with reaction. Irreversible and reversible reaction processes and comb model. Solutions for a reaction processes in a comb model. Anomalous diffusion and reaction processes on backbone structure. |
S1007570420300538 | Analytic solutions in implicit form are derived for a nonlinear partial differential equation with fractional derivative elements which can model the dynamics of a deterministically excited Euler Bernoulli beam resting on a viscoelastic foundation . Specifically the initial boundary value problem for the corresponding PDE is reduced to an initial value problem for a nonlinear ordinary differential equation in a Hilbert space . Next by employing the cosine and sine families of operators a variation of parameters representation of the solution map is introduced . Due to the presence of a nonlinear term a local fixed point theorem is employed to prove the local existence and uniqueness of the solution . Relying on the regularity properties of cosine and sine families taking into account the form of the nonlinear term and considering the properties of the fractional derivative the solution map of the abstract problem is cast into a derivative free analytic solution in implicit form for the initial boundary value problem . Results corresponding to the limiting purely elastic and purely viscous cases are also provided . The herein developed technique and derived implicit form solutions can be construed as generalizations of available results in the literature to account for fractional derivative elements . This is of significant importance given the vast utilization of fractional calculus modeling in modern engineering mechanics and in viscoelastic material behavior in particular . | A deterministically excited nonlinear fractional Euler Bernoulli beam is studied. A derivative free analytic solution in implicit form is provided. The limiting purely elastic and purely viscous cases are also provided. Important results given the vast use of fractional calculus modeling in engineering. |
S1007570420300551 | In order to explore the impacts of the time delayed velocity difference and backward looking effect on traffic flow this paper proposes an improved car following model based on the full velocity difference model by accounting for the time delayed velocity difference and backward looking effect . The linear stability condition of the proposed model is derived by taking advantage of the linear stability theory . The time dependent Ginzburg Landau equation and the modified Korteweg de Vries equation are established based on the nonlinear theory to describe the evolution of the traffic density waves near the critical stability point . Moreover the link between the TDGL and mKdV equations is also provided . Finally the results from both the numerical simulation and the theoretical analysis show that the proposed model can not only strengthen the stability of traffic flow but also suppress the traffic congestion . | an improved car following model considering the impacts of the time delayed velocity difference and backward looking effect on traffic flow is proposed. The extended models linear stability is obtained by applying the linear stability theory. Through nonlinear analysis the time dependent Ginzburg Landau TDGL equation and the modified Korteweg de Vries mKdV equation are derived. Numerical simulation shows that not only the results are closer to the actual traffic but also the stability of traffic flow can be enhanced. |
S1007570420300563 | In this paper we investigate the European option pricing problem under a regime switching FMLS model . This model is not only able to capture the main characteristics of asset returns it also incorporates the effect of regime switching being consistent with market observations . However option prices under this model are governed by a coupled FPDE system and the difficulty in seeking for analytical solution arises from the combination of the coupled system and the spatial fractional derivative . To deal with this difficulty we develop a two step solution procedure we firstly assume that the future information of the Markov chain is known and we derive the conditional option price by analytically solving a time dependent FPDE based on which an exact and explicit pricing formula for the unconditioned price is successfully worked out by using the Fourier cosine series expansion . It is also shown through the numerical experiments that it converges very rapidly and has potential to be applied in practice . | European option pricing is considered under a regime switching FMLS model. A two step solution procedure is developed to solve the coupled FPDE system. An exact and explicit pricing formula is presented based on Fourier cosine series. |
S1007570420300575 | In this paper we study the phenomena of the extinction and persistence of predator populations of the three dimensional Kooi etal . model in the global formulation of the problem . This model contains three populations prey susceptible predators and infected predators . We compute ultimate sizes of interacting populations and establish that all biologically feasible trajectories eventually enter in some bounded domain and remain there . We derive analytical conditions for the extinction of the infected predator population in cases of different equal mortality rates of predators . In particular we find conditions under which 1 the population of prey persists while both of predator populations die out 2 the populations of prey and susceptible predators persist while the population of infected predators dies out . Besides we describe the case when at least one periodic orbit exists in the disease free invariant plane . Our analysis is based on using the localization method of compact invariant sets and the theorem of LaSalle . Main theoretical results are illustrated by numerical simulation . | Convergence dynamics of one eco epidemiological model is studied. Ultimate sizes of prey and predator populations are computed. Conditions for extinction of infected predators are derived. Conditions for persistence of susceptible predators are derived. Cases of different equal death rates of predators are examined. |
S1007570420300587 | There are several theoretically well posed models for the AllenCahn equation under mass conservation . The conservative property is a gift from the additional nonlocal term playing a role of a Lagrange multiplier . However the same term destroys the boundedness property that the original AllenCahn equation presents The solution is bounded by 1 with an initial datum bounded by 1 . In this paper we propose a novel mass conserving AllenCahn equation and prove the existence and uniqueness of a classical solution in the context of the theory of analytic semigroups as well as the boundedness property of the solution . From the numerical point of view we investigate a linear unconditionally energy stable splitting scheme of the proposed model for the boundedness of numerical solutions . Various numerical experiments are presented to demonstrate the validity of the proposed method and to make distinctions from a few closely related methods . | A novel mass conserving Allen Cahn equation with a periodic boundary condition is proposed and analyzed. We prove the existence and uniqueness of a solution for the proposed mass conserving equation. The proposed equation confirms the boundedness of solutions as well. Various numerical experiments are presented to demonstrate the validity of the proposed method. Comparison experiments make clear distinctions from a few closely related methods. |
S1007570420300599 | The Rate Control Protocol uses explicit feedback from routers to control network congestion . RCP estimates its fair rate from two forms of feedback rate mismatch and queue size . An important design question that remains open in RCP is whether the presence of queue size feedback is helpful given the presence of feedback from rate mismatch . The feedback from routers to end systems is time delayed and may introduce instabilities and complex nonlinear dynamics . Delay dynamical systems are often modeled using delay differential equations to facilitate a mathematical analysis of their performance and dynamics . The RCP models with and without queue size feedback give rise to two distinct nonlinear delay differential equations . Earlier work on this design question was based on methods of linear systems theory . For further progress it is quite natural to employ nonlinear techniques . In this study we approach this design question using tools from control and bifurcation theory . The analytical results reveal that the removal of queue feedback could enhance both stability and convergence properties . Further using Poincar normal forms and center manifold theory we investigate two nonlinear properties namely the type of the Hopf bifurcation and the asymptotic stability of the bifurcating limit cycles . We show that the presence of queue feedback in the RCP can lead to a sub critical Hopf bifurcation which would give rise either to the onset of large amplitude limit cycles or to unstable limit cycles . Whereas in the absence of queue feedback the Hopf bifurcation is always super critical and the bifurcating limit cycles are stable . The analysis is complemented with computations and some packet level simulations as well . In terms of design our study suggests that the presence of both forms of feedback may be detrimental to the performance of RCP . | Using tools from control and bifurcation theory we study whether the queue size feedback in Rate Control Protocol RCP is useful. We conduct stability convergence and bifurcation analysis for RCP with and without queue size feedback. Removal of queue size feedback could enhance both the stability and convergence properties of RCP. The presence of queue size feedback in RCP can lead to a sub critical Hopf bifurcation which is undesirable. Queue size feedback is detrimental to the performance of the RCP protocol. |
S1007570420300605 | We make a detailed numerical study of a three dimensional dissipative vector field derived from the normal form for a cusp Hopf bifurcation . The vector field exhibits a NeimarkSacker bifurcation giving rise to an attracting invariant torus . Our main goals are to follow the torus via parameter continuation from its appearance to its disappearance studying its dynamics between these events and to study the embeddings of the stable unstable manifolds of the hyperbolic equilibrium solutions over this parameter range focusing on their role as transport barriers and their participation in global bifurcations . Taken together the results highlight the main features of the global dynamics of the system . | This work presents a detailed numerical study of the dynamics of a three dimensional dissipative vector field exhibiting a NeimarkSacker bifurcation. We follow the attracting invariant torus resulting from this bifurca tion until its destruction and the subsequent appearance of a chaotic attractor. We provide a reliable method for computation and visualization of a resonant torus especially in the regime where the torus is only a C. invariant object. We study the stable unstable manifolds of the equilibrium solutions which act as separatrices transport barriers for the system. The numerical study results in a number of conjectures about the global dynamics of the system which we formalize in the conclusions. |
S1007570420300617 | Lasota and Myjak demonstrated that one can study attractors to an iterated function system possibly containing discontinuous functions . We continue this line of thought by working with IFS with a lower semicontinuous Hutchinson Barnsley operator and two new types of attractors the small attractor and minimal attractors . We characterize exactly when an IFS possesses a small attractor and provide several practically verifiable sufficient conditions for this . To study minimal attractors we create the notion of the weak basin we show a minimal attractor behaves much like a small attractor on its weak basin and that the weak basin is the largest set in which a minimal attractor behaves like this . We then give a characterization of when the weak basin is open . Further we show that when the iterates of the Hutchinson Barnsley operator of an IFS form an equicontinuous set of multifunctions both the weak basin and the point wise basin is closed . | Characterized when an iterated function system IFS posses a small attractor. We show that minimal attractors and small attractors admit a basin of attraction called the weak basin. We found under certain conditions the pointwise basin of a pointwise attractor is the entire space. |
S1007570420300629 | Co infections by multiple pathogens have important implications in many aspects of health epidemiology and evolution . However how to disentangle the non linear dynamics of the immune response when two infections take place at the same time is largely unexplored . Using data sets of the immune response during influenza pneumococcal co infection in mice we employ here topological data analysis to simplify and visualise high dimensional data sets . | The mapper algorithm is a topological data analysis technique used for the qualitative analysis of biological data. Simplification and visualisation of high dimensional data sets and nonlinearities. We find persistent shapes of the data in the three infection scenarios. |
S1007570420300630 | We introduce a new general class of nonlinear variable order fractional partial differential equations . The NVOFPDE contains as special cases several partial differential equations such as the nonlinear variable order fractional equations usually denoted as Klein Gordon diffusion wave and convection diffusion wave . To find the numerical solution of the NVOFPDE we formulate a novel class of basis functions called generalized shifted Chebyshev polynomials that includes the shifted Chebyshev polynomials as a particular case . The solution of the NVOFPDE is expanded following the GSCP and the corresponding operational matrices of VO fractional derivatives in the Caputo type are obtained . An optimization method based on the GSCP and the Lagrange multipliers converts the problem into a system of nonlinear algebraic equations . The convergence analysis is guaranteed through a theorem concerning the GSCP and several numerical examples confirm the precision of the method . | This paper introduces a new general class of nonlinear variable order fractional partial differential equations NVOFPDE that contains as special cases several partial differential equations such as the nonlinear variable order fractional equations usually denoted as KleinGordon diffusion wave and convection diffusion wave. Shifted Chebyshev polynomials SCP are developed to the new family of basis functions namely generalized shifted Chebyshev polynomials GSCP . A new variable order fractional operational matrix in the Caputo type for the GSCP is derived. A new optimization method based on the GSCP with the help of the Lagrange multipliers is proposed for the NVOFPDE. The defined GSCP rather SCP needs less basis functions to provide satisfactory results with the same level of accuracy. |
S1007570420300642 | The lumped mass model is derived from a one mode Galerkin discretization with the GaussLobatto quadrature applied to the non linear swelling pressure term . Our reduced order model of the problem is then analyzed to study the essential dynamics of an elastic cantilever EulerBernoulli beam subject to the swelling pressure described by Grobs law . The solutions to the initial value problem for the resulting nonlinear ODE are proved to be always periodic . The numerical solution to the derived lumped mass model satisfactorily matches the finite difference solution of the dynamic beam problem . Including the effect of oscillations at the base of the beam we show that the model exhibits resonances that may crucially influence its dynamical behavior . | Cantilever beam. Swelling pressure. Lumped mass model. Periodic solution and Resonances. |
S1007570420300654 | We study scaling features in the reactions of cereral blood vessel network to sudden jumps in peripheral arterial pressure in rats . Using laser speckle contrast imaging to measure the relative velocity of cerebral blood flow and detrended fluctuation analysis for processing experimental data we investigate distinctions in the responses of veins and capillaries . To quantify short term reactions associated with transients we propose an extension of the conventional DFA approach which estimates an additional scaling exponent reflecting the effect of nonstationarity . We also consider the ability of characterizing vascular dynamics with multifractal DFA in terms of the degree of multiscality . Based on statistical analysis we report significant distinctions in the responses of small network of microcerebral blood vessels compared to veins such as the sagittal sinus which are quite insensitive to variations in peripheral blood circulation . | Reactions of cerebral blood circulation to jumps in peripheral arterial pressure are studied. An extension of the conventional DFA approach is proposed. Significant distinctions in the responses of cerebral blood vessels are reported. |
S1007570420300666 | A new type of spiral wave caused by the pitchfork bifurcation of a limit cycle is reported which may exist in ecosystems containing two species that are not symbiotic . The dynamical behavior of the spiral wave is explained by a superposition principle of disturbance intensity vectors in oscillatory media . This type of spiral wave is characterized by a slow moving line defect that passes through the spiral center . The line defect disturbs the local phase waves whose disturbance can be superposed with the disturbance coming from the spiral core . This superposition principle of disturbance intensity vectors provides a new theory and method for studying the pattern formation in oscillation media . On the one hand our findings shed light on the dynamics of the pattern formation on the other we predict a type of spiral wave which has not been found in nature or laboratories to date and provide directions and guidances for ecological researches about ecosystems containing two species that are not symbiotic . | A new type of spiral wave is reported which may exist in ecosystems containing two or more species that are not symbiotic. A line defect that passing through the spiral center moves very slowly which disturbs the local phase waves. The disturbance of the line defect can be superposed with the disturbance coming from the spiral core. A superposition principle of disturbance intensity vectors is presented. |
S1007570420300678 | Van der Pol and Rayleigh oscillators are two traditional paradigms of nonlinear dynamics . They can be subsumed into a general form of LinardLevinsonSmith system . Based on a recipe for finding out maximum number of limit cycles possible for a class of LLS oscillator we propose here a scheme for systematic designing of generalised Rayleigh and Van der Pol families of oscillators with a desired number of multiple limit cycles . Numerical simulations are explicitly carried out for systematic search of the parameter space for bi rhythmic and tri rhythmic systems and their higher order variants . | Based on a general scheme of counting limit cycle of a given LLS equation we have proposed a recipe for multi rhythmicity. For polynomial damping and restoring force functions we have constructed birhythmic and tri rhythmic oscillators of Van der Pol and Rayleigh families. New alternative generalizations of Van der Pol and Rayleigh families of bi rhythmicity and tri rhythmicity. The scheme is used to simulate the valid range of parameters for realizing limit cycle oscillations with different generalizations of bi rhythmic and tri rhythmic Rayleigh and Van der Pol families. As multi rhythmicity plays an important role in switching transitions between different dynamical states its control and manipulation would be useful. |
S100757042030068X | The reported efficacy of biofeedback is not consistent across studies . One issue that has not been addressed in previous studies is the effect of the reference signal in a biofeedback system . | We have used the concept of time delayed feedback control to introduce a new reference signal in biofeedback systems. A computational black box model was developed to show the nonlinear behavior of human response time. The effect of two different reference signals using a computational model and human experiments were investigated. It seems that the reference signal in biofeedback systems should be modified based on the characteristics of individuals. |
S1007570420300691 | In this work we revisit a classical problem of traveling waves in a damped FrenkelKontorova lattice driven by a constant external force . We compute these solutions as fixed points of a nonlinear map and obtain the corresponding kinetic relation between the driving force and the velocity of the wave for different values of the damping coefficient . We show that the kinetic curve can become | Traveling waves in a damped driven FrenkelKontorova lattice are computed. Force velocity kinetic relation can be non monotone and multivalued. Stability of the obtained solutions is investigated via Floquet analysis. Decreasing portions of the kinetic curve always bear an unstable eigendirection. |
S1007570420300721 | In this paper finite time synchronization issue of fractional order complex valued dynamical networks with multiple weights is addressed . Multiple weights are pulled into consideration which makes our model more practical and general than single weight one . Combining Lyapunov method with graph theoretic method and making use of the theory of complex functions finite time synchronization criteria for fractional order complex valued dynamical networks with multiple weights are established by using feedback control and adaptive control respectively . Furthermore the settling time of synchronization is effectively estimated which is connected with the order of fractional derivative the parameters of control and topological structure of networks . Eventually numerical simulations are exhibited to demonstrate the validity of theoretical results and analyse the relationship between the settling time of synchronization and the order of fractional derivative with the parameters of control . | Multiple weights are considered into FCDNs as the initial attempt which makes the model more realistic in practical applications. A finite time synchronization criterion based on adaptive control for FCDNs is derived for the first time. Settling time of synchronization depends on the order of fractional derivative the parameters of control and topologica structure of networks. |
S1007570420300745 | In artificial neural networks the diffusion phenomenon of electrons exists inevitably due to the electromagnetic field of neural networks is heterogeneous . In this paper we study the spatio temporal dynamical behaviors of a reaction diffusion neural network with leakage delay . By analyzing the corresponding characteristic equation the sufficient and necessary conditions of Turing instability are obtained and the existence of Turing Hopf and Turing Hopf bifurcations is also established . Furthermore the truncated normal form up to third order is derived to understand and classify the spatio temporal dynamics close to the Turing Hopf bifurcation point . By numerical simulations we find a pair of spatially inhomogeneous periodic solutions and illustrate the effects of time delays and spatial diffusion on the spatio temporal dynamics of the model . | The spatio temporal dynamics of a reaction diffusion neural network with leakage delay is studied. The sufficient and necessary conditions of Turing instability are obtained. The truncated normal form is derived to understand and classify the spatio temporal dynamics close to the Turing Hopf bifurcation point. A pair of spatial inhomogeneous periodic solutions of the system are found. |
S1007570420300757 | We show that the integrable equations of hydrodynamic type admit nonlocal reductions . We first construct such reductions for a general Lax equation and then give several examples . The reduced nonlocal equations are of hydrodynamic type and integrable . They admit Lax representations and hence possess infinitely many conserved quantities . | All possible nonlocal reductions of the hydrodynamic type of equations in. dimensions are constructed. It is noted that such reductions are possible only for all even numbered systems. Examples of nonlocal reductions for hydrodynamic type of equations are given. It is explored that the reduced nonlocal equations are of hydrodynamic type and integrable that is they admit Lax representations and so possess infinitely many conserved quantities. Some examples of conserved quantities of the new nonlocal reduced systems are given. |
S1007570420300770 | We study coupled unstaggered staggered soliton pairs emergent from a system of two coupled discrete nonlinear Schrdinger equations with the self attractive on site self phase modulation nonlinearity coupled by the repulsive cross phase modulation interaction on 1D and 2D lattice domains . These mixed modes are of a symbiotic type as each component in isolation may only carry ordinary unstaggered solitons . While most work on DNLS systems addressed symmetric on site centered fundamental solitons these models give rise to a variety of other excited states which may also be stable . The simplest among them are antisymmetric states in the form of discrete twisted solitons which have no counterparts in the continuum limit . In the extension to 2D lattice domains a natural counterpart of the twisted states are vortical solitons . We first introduce a variational approximation for the solitons and then correct it numerically to construct exact stationary solutions which are then used as initial conditions for simulations to check if the stationary states persist under time evolution . Two component solutions obtained include 1D fundamental twisted and twisted twisted soliton pairs 2D fundamental fundamental soliton pairs and 2D vortical vortical soliton pairs . We also highlight a variety of other transient dynamical regimes such as breathers and amplitude death . The findings apply to modeling binary Bose Einstein condensates loaded in a deep lattice potential with identical or different atomic masses of the two components and arrays of bimodal optical waveguides . | Unstaggered staggered soliton pairs observed in 1D and 2D DNLS. Antisymmetric states in the form of discrete twisted solitons are observed in 1D. Fundamental and vortical soliton pairs are observed in 2D. Findings are relevant to lattice BECs and arrays of bimodal optical waveguides. |
S1007570420300782 | This paper attempts to investigate the stochastic resonance phenomenon in a delay controlled dissipative bistable potential with time delayed feedback under the action of harmonic excitation and additive noise by using small delay approximation theory and signal to noise ratio theory . The time delay and feedback strength are able to adjust the potential shapes precisely by fusing potential parameters . Moreover the steady state probability distribution and output SNR are derived to demonstrate that time delayed feedback is able to control and improve the SR for enhancing the useful signal embedded in a noisy signal where moderate time delay and feedback strength can maximize the output SNR . Therefore a controlled SR method via time delayed feedback is proposed to enhance useful signals embedded in mechanical signals for mechanical fault diagnosis where the widely used frequency shifted and rescaling transform is used to preprocess large parameter vibration signals of double row cylindrical bearings . The experimental results indicate that the controlled SR method via time delayed feedback can enhance the useful signal embedded in the vibration signal from double row cylindrical bearings where its amplitude is amplified up to tenfold than that in the envelope spectrum of raw signal . | SR in a delay controlled dissipative bistable potential with time delayed feedback is investigated. A controlled SR method via time delayed feedback is proposed to enhance useful signals embedded in mechanical signals. Experimental results show the effectiveness of the proposed delay controlled SR method. |
S1007570420300800 | We study coupled Gauss maps in one dimension and observe a transition to band periodic state with 2 bands . This is a periodic state with period 2 in a coarse grained sense . This state does not show any long range order in space . We compute two different order parameters to quantify the transition a Flipping rate | We observe directed percolation DP transition to the absorbing state in a coupled Gaussian maps. It reaches a coarse grained period 2 state in time. It has no long range spatial order even in a coarse grained sense. We propose flip rate F t fraction of sites which don t return to the same band after two time steps as an order parameter. Estimates of decay exponent of F t persistence exponent as well as of z and v put the transition firmly in DP class. |
S1007570420300812 | The purpose of this paper is to examine a special kind of game option whose main feature is the presence of an early exercise right for the seller as well as for the buyer . The seller has to pay some amount above the usual option payment for this right . Usually this penalty payment is presented by a constant amount during the option life . Alternatively in this paper we present the cancellation payment as the usual option payment multiplied by a constant . We introduce also a discount factor which gives a benefit for early exercising . It is closely related to the existence of a continuous dividend payment . In that way we can describe a dividend model in our framework . | We examine put and call perpetual game options. The sellers penalty is proportional to the usual option payment. We determine the optimal exercise regions for both participants. We derive the equations for the exercise boundaries. We obtain the fair option prices and give some numerical examples. |
S1007570420300848 | In this paper the scattering between the non topological kinks arising in a family of two component scalar field theory models is analyzed . A winding charge is carried by these defects . As a consequence two different classes of kink scattering processes emerge collisions between kinks that carry the same winding number and scattering events between kinks with opposite winding number . The variety of scattering channels is very rich and it strongly depends on the collision velocity and the model parameter . For the first type of events four distinct scattering channels are found | Kink scattering in a 1 1 relativistic two scalar field theory is analyzed. Non topological kinks are analytically identified in the model. The kinks carry a winding charge. The collisions between kinks with the same or opposite winding charge are described. The dependence of the scattering channels on the collision velocity is analyzed. |
S100757042030085X | The dynamics of solar sail maneuvers are conceptually different from classical control maneuvers where one considers impulsive changes in the velocity of a spacecraft . Solar sail orbits are continuous in both position and velocity in a varying vectorfield opening the possibility of the existence of heteroclinic connections by means of artificially changing the vectorfield with a sail maneuver . This paper investigates solar sail assisted maneuvers to obtain families of artificial heteroclinic connections between Lissajous libration point orbits . The study is based on a careful analysis of the geometry of the phase space of the linearized equations around the equilibrium points the dynamical identification of the main parameters and the representation of the solutions in the action angle variables . We identify the main dynamical properties of the connecting families presenting systematic new options for the mission analysis in the libration point regime using this technology including a methodology to approach the classical problem of exclusion zone avoidance . | 3 D Artificial Libration Point which consider the influence of cone angle clock angle and lightness parameter. Investigates propellant free transfers between libration point orbits using solar sailing. The study is based on a careful analysis of the geometry of the phase space of the linearized equations around the equilibrium points the dynamical identification of the main parameters and the representation of the solutions in the action angle variables. Use the effective phases plane EPP to calculate the transfer trajectory to avoid the exclusion zones. |
S1007570420300861 | This paper proposes the concept of Razumikhin type functional differential inequalities and points out that certain quantitative properties can be established for the Razumikhin type functional differential inequalities . By virtue of certain auxiliary functions some fundamental results on the quantitative bounds for the Razumikhin type functional differential inequalities are systemically established in the paper and these bounds are applied to deduce the basic Razumikhin type stability theorems including those for It | Explicitly propose the concept of Razumikhin type functional differential inequalities RFDIs for the first time. Propose a more relaxed condition for studying quantitative bounds for the RFDIs. Establish general and uniform bounds for general Razumikhin type differential inequalities. Present new more direct approach to deduce some basic Razumikhin type stability results than the classical ones. |
S1007570420300873 | In this paper modified Zakharov Kuznetsov equation is taken into consideration . Diverse variety of solitonic structures are computed by using extended algebraic method . Sufficient conditions for the existence of the computed solutions are presented . Then Galilean transformation is utilized to transform the considered model in the planer dynamical system . All possible forms of phase portraits with respect to the parameters are plotted . Moreover we utilized the numerical techniques to find out the nonlinear periodic structures of the discussed model and results are shown graphically . Moreover after deploying an extrinsic periodic force the effect of frequency is observed then sensitive analysis is applied for different initial value problems to analyze the quasiperiodic and chaotic behaviour . In addition to this Lie point symmetries and their corresponding conservation laws are reported at the end . | Solitonic structures of Zakharov Kuznetsov mZK equation. Transformation of the considered model in the planer dynamical system. Quasiperiodic and chaotic behavior of the mZk equation. Conservation laws of mZK equation via Lie symmetry. |
S1007570420300885 | Recently a novel bifurcation technique known as deflated continuation was applied to the single component nonlinear Schrdinger equation with a parabolic trap in two spatial dimensions . This bifurcation analysis revealed previously unknown solutions shedding light on this fundamental problem in the physics of ultracold atoms . In the present work we take this a step further by applying deflated continuation to two coupled NLS equations which feature a considerably more complex landscape of solutions . Upon identifying branches of solutions we construct the relevant bifurcation diagrams and perform spectral stability analysis to identify parametric regimes of stability and instability and to understand the mechanisms by which these branches emerge . The method reveals a remarkable wealth of solutions . These include both well known states arising from the Cartesian and polar small amplitude limits of the underlying linear problem but also a significant number of more complex states that arise through bifurcations . | A two component two dimensional nonlinear Schrdinger system with a parabolic potential is considered. Deflated continuation method is applied to the above system and the deflated operator is adjusted to eliminate rotations of solutions. Branches of solutions are obtained which some of them are found in the literature but others correspond to previously unknown ones. Linear stability analysis is performed by using state of the art eigenvalue solvers. A cartography of possible solutions is presented. |
S1007570420300897 | Recently many algorithms have emerged inspired by the biological behavior of animal life to deal with complicated applications such as combinatorial optimization . One of the most critical discussions involving these algorithms is concerning their objective functions . Also recently many works have demonstrated the efficiency of Tsallis non extensive statistics in several applications . However this formalism has not yet been tested in most recent bio inspired algorithms as an evaluation function . Thus this paper presents a study of seven of the most promising bio inspired algorithms recently proposed from this entropy applied to the multi thresholding segmentation of medical images . The results show the range of values of | In this article we study the latest bio inspired algorithms that emerged in at most a decade ago. These algorithms are studied from the point of view of medical image segmentation based on multi thresholding which is a challenger with high computational time. In our paper the evaluation functions used in these algorithms are based on the non extensive Tsallis entropy which has been demonstrated its efficiency in several physical systems. However for most of the algorithms studied here the application of this type of entropy as an evaluation function had not yet been tried. |
S1007570420300915 | Based on the time frequency analysis a piecewise re scaled method is proposed to realize aperiodic resonance in a Duffing system excited by the nonlinear frequency modulated signal . Based on the aperiodic resonance theory the weak NLFM signal is enhanced greatly . By short time Fourier transform numerical simulations are carried out for several kinds of NLFM signal . The results show that the method enhances the NLFM signal effectively . Meanwhile the effectiveness of the method is still illustrated in the noise background . In addition the noise and the interference frequency can be removed . Noteworthy and differently as what happens with the stochastic resonance and vibrational resonance the aperiodic resonance does not require any auxiliary signal or noise to induce it . This constitutes also a new result of this paper . Next in order to expand the application of this method it is used to process the experiment signal of bearing fault under variable speed condition . The validity of the method is illustrated again . The results provide new reference in processing non stationary frequency modulated signal . Finally an adaptive piecewise re scaled aperiodic resonance scheme is put forward to get optimal parameters to induce stronger aperiodic resonance quickly . | Strong aperiodic resonance is realized in NLFM signal excited nonlinear system. Different NLFM signals are enhanced by the aperiodic resonance. The proposed method can remove the background noise and interference frequency. The experimental signal is processed by aperiodic resonance to enhance the fault characteristic information of mechanical equipment with variable speed. |
S1007570420300939 | The cylindrical Kadomtsev Petviashvili equation related to cylindrical geometry as one type of the variable coefficient KP equation is widely used to describe nonlinear phenomena in fluid plasma and other fields . With symbolic computation we have derived the multi soliton solutions rational solutions lump solutions and interaction solutions to the cKP equation based on its bilinear representation . The interaction solutions include two types The interaction between lump and stripe and the interaction between lump and soliton . Moreover we have proposed a new approach to search for the interaction solutions which can decrease the complexity of the associated nonlinear algebraic equations via reducing the number of the variables . The fast calculation approach provides the condition for the predictability of the interaction solution . | A new approach is proposed to search for the interaction solutions which can decrease the complexity of the associated nonlinear algebraic equations via reducing the number of the variables. The fast calculation approach provides the condition for the predictability of the interaction solution. Interaction phenomena between lump wave and a stipe and lump wave and soliton solution are discussed and numerically simulated. |
S1007570420301039 | We consider a modification of the well studied Hamiltonian Mean Field model with cosine potential by introducing a hard core point like repulsive interaction and propose a numerical integration scheme to integrate its dynamics . Our results show that the outcome of the initial violent relaxation is altered and also that the phase diagram is modified with a critical temperature at a higher value than in its counterpart without hard core collisions . | Systems with long range interactions have drawn a great deal of attention over the last few decades not only because they are common in nature e.g. self gravitating systems and charged plasmas but also due to many unusual phenomena not observed in short range interacting systems. In the present paper we discuss for the Hamiltonian mean field model a much studied system the effects on the system dynamics of the introduction of a hard core point like interaction resulting in a system with both global and strong short range interactions. We developed a numeric algorithm for the molecular dynamics of this type of mixed interaction and applied it to understand how the violent relaxation and the long term dynamics are altered. This is a first and original step to understand how the special phenomenology of long range interacting systems is altered by hard core potentials and point to new research and relevant open problems. |
S1007570420301040 | In this work we propose the Fisher DisEn plane by the discrete Fisher information measure and dispersion entropy to analyze complex dynamic systems . Multiple trials with different artificial chaos and noises are carried out regarding their capability on distinguishing different levels of chaos distinguishing different chaos distinguishing different noise distinguishing between chaos and noise . Compared with the original complexity entropy causality plane our method is more superior in extracting more subtle details to distinguish different dynamic systems . In the experiments with the financial series our method is found to be more reasonable in discriminating stock markets from different parts of the world by making comparisons with original method . | We propose the Fish DisEn plane to analyze time series from complex dynamic systems. The new approach is capable of extracting more detailed information from time series. We apply our proposed method to the simulated time series to test the validity of distinguishing different chaos and noises. Our method is more reasonable in discriminating stock markets from different parts of the world by making comparison with original method. |
S1007570420301052 | The complexity entropy causal plane has been widely discussed recently . It can measure the information of sequences from two perspectives to reflect their structural details . But in experiments we find that as a method based on probability space the original CECP is not sensitive to the shape of the probability distributions which may lead to inaccurate structural feature differentiation . Therefore we propose a novel normalized complexity entropy causal plane based on the modified Fisher information measure to solve the problem . The modified Fisher information measure and divergence score | The novel statistics NF CECP focuses more on the shape of the probability distributions amplitude of signals and other information regarding to the structure. NF CECP can distinguish Gaussian white noises GWN from ARFIMA sequences but the original CECP fails. It also shows that in the past 15 years the relative values of CF and MF of the two countries are gradually approaching and it can be considered that the financial relationship between the two countries may be getting closer. |
S1007570420301064 | This paper is devoted to elucidating a sufficient condition under which Mackey Glass type discrete hematopoiesis models have at least two positive periodic solutions . This model has periodic coefficients and time delays and includes several production function terms that act as feedback . Our result is obtained by applying the Krasnoselskii fixed point theorem and is represented by a relationship between period coefficients and the production function . Example and its simulations are attached to show how to apply our result . In this example there are exactly two positive 3 periodic solutions in the hematopoiesis model . Simulation shows that one periodic solution is stable and the other is unstable . It also shows that our result can be improved by weakening assumptions about the production function . | To elucidate the dynamics of blood cells hematopoiesis models having a unimodal production function that acts as feedback are considered. Our model is described by a first order nonlinear difference equation with periodic coefficients and time delays. Periodic behavior of the density of mature blood cells is investigated. The result obtained is described by an easily identifiable relational expression relating to periodic coefficients and the production function. Using Krasnoselskii fixed point theorem the existence of multiple positive periodic solutions is revealed. |
S1007570420301076 | In this paper a stability analysis for a Cournot duopoly model with tax evasion and time delay in a continuous time framework is presented . The mathematical model under consideration follows a gradient dynamics approach is nonlinear and four dimensional with state variables given by the production and declared revenue of each competitor . We prove that both the marginal cost rate and time delay play roles as bifurcation parameters . More precisely if the marginal cost rate lies in certain closed interval then the equilibrium point is delay independent stable otherwise it is delay dependent stable and a Hopf bifurcation necessarily occurs . Some numerical simulations are presented in order to confirm the proposed theoretical results and illustrate the effect of the bifurcation parameters on model stability . | A stability analysis for a Cournot duopoly model with tax evasion and time delay is presented. The mathematical model under consideration follows a gradient dynamics approach is non linear and four dimensional. The marginal cost rate belongs to a closed interval if and only if the system is delay independent stable. When the system is delay dependent stable a Hopf bifurcation occurs. Simulations and graphs to illustrate the theoretical results are presented. |
S1007570420301106 | The dimensional incompressible and barotropic magnetohydrodynamic flow is studied combined with qualitative and quantitative analysis . The conservation of the energy of this system and the global existence of the solution | The qualitative and quantitative analysis of MHD equations that possessing strong physical background is presented. The global existence of the solution Lie symmetry analysis and the conservation law of MHD equations are obtained. The study provides a macroscopic grasp as well as specific analysis of the form and behavior of the nonlinear MHD system. |
S1007570420301118 | Hysteresis is a special type of behavior found in many areas including magnetism mechanics biology economics etc . One of the characteristics of hysteresis systems is that they are approximately rate independent for slow inputs . It is possible to express this characteristic in mathematical language by decomposing hysteresis operators as the sum of a rate independent component and a nonhysteretic component which vanishes in steady state for slow inputs . This decomposition called | Hysteresis systems are approximately rate independent for slow inputs. Hysteresis systems are causal. This paper presents a new decomposition of hysteresis operators into a. rate independent component and a. nonhysteretic component that vanishes for slow inputs. |
S1007570420301131 | In this paper we propose a new two stage methodology which is a hybrid model based on ensemble empirical mode decomposition to predict the complex financial time series . The hybrid model comprises Multidimensional | Using weighted Euclidean distance to match patterns have higher accuracy than Euclidean distance. MKNN method is effective for predicting high frequency IMFs. ARMA model is effective for predicting low frequency IMFs. In the prediction of the residual wave quadratic regression model is simple and effective. |
S1007570420301143 | We study the classical chaotic scattering of a He atom off a harmonically vibrating Cu surface . The three degree of freedom model is studied by first considering the non vibrating 2 dof model for different values of the energy . The set of singularities of the scattering functions shows the structure of the tangle between the stable and unstable manifolds of the fixed point at an infinite distance to the Cu surface in the Poincar map . These invariant manifolds of the 2 dof system and their tangle can be used as a starting point for the construction of the stable and unstable manifolds and their tangle for the 3 dof coupled model . When the surface vibrates the system has an extra closed degree of freedom and it is possible to represent the 3 dof tangle as deformation of a stack of 2 dof tangles where the stack parameter is the energy of the 2 dof system . Also for the 3 dof system the resulting invariant manifolds have the correct dimension to divide the constant total energy manifold . By this construction it is possible to understand the chaotic scattering phenomena for the 3 dof system from a geometric point of view . We explain the connection between the set of singularities of the scattering function the Jacobian determinant of the scattering function the relevant invariant manifolds in the scattering problem and the cross section as well as their behavior when the coupling due to the surface vibration is switched on . In particular we present in detail the relation between the changes as a function of the energy in the structure of the caustics in the cross section and the changes in the zero level set of the Jacobian determinant of the scattering function . | The singularities of scattering functions detect stable and unstable manifolds. Stable and unstable manifolds direct dynamics and are robust under perturbations. Poincare map of the 3 dof system is built with a stack of the 2 dof Poincare maps. Cross section is the projection of graph of scattering function in its domain. Caustics change if the Jacobian determinant of the scattering function change. |
S1007570420301155 | We reveal the networks of simple symmetric periodic orbits in a double barred galaxy model . Specifically we investigate the dependence on the total orbital energy of the positions but also on the stability of the periodic solutions . For every orbital family we also compute the horizontal and vertical critical parameter values of the system at which new periodic families bifurcate from . Of particular interest are the vertical critical points which act as starting points for the creation of new families of three dimensional periodic orbits . The atlas of the simple periodic trajectories is presented in the | We use a new analytical model for describing the motion of stars in double barred galaxies. We reveal the networks of simple symmetric periodic orbits of the system. The critical solutions of the system which are bifurcation points are determined. |
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