The mean first-passage time of a bistable system with time-delayed feedback driven by multiplicative non-Gaussian noise and additive Gaussian white noise is investigated. Firstly, the non-Markov process is reduced to ...The mean first-passage time of a bistable system with time-delayed feedback driven by multiplicative non-Gaussian noise and additive Gaussian white noise is investigated. Firstly, the non-Markov process is reduced to the Markov process through a path-integral approach; Secondly, the approximate Fokker-Planck equation is obtained by applying the unified coloured noise approximation, the small time delay approximation and the Novikov Theorem. The functional analysis and simplification are employed to obtain the approximate expressions of MFPT. The effects of non-Gaussian parameter （measures deviation from Gaussian character） r, the delay time τ, the noise correlation time to, the intensities D and a of noise on the MFPT are discussed. It is found that the escape time could be reduced by increasing the delay time τ, the noise correlation time τ0, or by reducing the intensities D and α. As far as we know, this is the first time to consider the effect of delay time on the mean first-passage time in the stochastic dynamical system.展开更多
In this paper we propose a two-layer emergent model for scalable swarm system. The first layer describes the indi-vidual flocking behavior to the local goal position (the center of minimal circumcircle decided by the ...In this paper we propose a two-layer emergent model for scalable swarm system. The first layer describes the indi-vidual flocking behavior to the local goal position (the center of minimal circumcircle decided by the neighbors in the positive visual set of individuals) resulting from the individual motion to one or two farthest neighbors in its positive visual set; the second layer describes the emergent aggregating swarm behavior resulting from the individual motion to its local goal position. The scale of the swarm will not be limited because only local individual information is used for modelling in the two-layer topology. We study the stability properties of the swarm emergent behavior based on Lyapunov stability theory. Simulations showed that the swarm system can converge to goal regions while maintaining cohesiveness.展开更多
The asymmetric effects on the escape rates from the stable states x±in the bistable system are analyzed. The results indicate that the multiplicative noise and the additive noise always enhance the particle escap...The asymmetric effects on the escape rates from the stable states x±in the bistable system are analyzed. The results indicate that the multiplicative noise and the additive noise always enhance the particle escape from stable states x±of bistable.However,the asymmetric parameter r enhances the particle escape from stable state x_+,and holds back the particle escape from stable state x_-.展开更多
For a long time it was a common opinion that hyperbolic attractors are artificial mathematical constructions. However, in the recent papers there were proposed physically realizable systems that possess, in their phas...For a long time it was a common opinion that hyperbolic attractors are artificial mathematical constructions. However, in the recent papers there were proposed physically realizable systems that possess, in their phase space, the set with features that are very similar to hyperbolic type of attractors. As is known, invariant sets are called hyperbolic attractors of the dynamical system if they are closed, topologically transitive subsets, and every their trajectory possesses uniform hyperbolicity. Very familiar types of the hyperbolic attractors are Smale-Williams＇ solenoid and Plykin＇s attractor. Further, it is well known that chaotic systems are very sensitive to the external perturbations. This property is used for controlling nonlinear systems and chaos suppression. Thus, an important question arises： Is it possible to suppress chaos in systems with hyperbolic attractors because these attractors are structurally stable subsets？ In the present contribution we study the possibility of stabilization of chaotic oscillations in systems with the Smale-Williams hyperbolic attractors by means of the Pyragas method with a delay. It is shown that by means of external perturbation the dynamical system could be controllable： the hyperbolic attractor degenerates into a periodic one.展开更多
The authors consider systems of the form where the matrix A(u) is assumed to be strictly hyperbolic and with the property that the integral curves of the eigenvector fields are straight lines. For this class of system...The authors consider systems of the form where the matrix A(u) is assumed to be strictly hyperbolic and with the property that the integral curves of the eigenvector fields are straight lines. For this class of systems one can define a natural Riemann solver, and hence a Godunov scheme, which generalize the standard Riemann solver and Godunov scheme for conservative systems. This paper shows convergence and L1 stability for this scheme when applied to data with small total variation. The main step in the proof is to estimate the increase in the total variation produced by the scheme due to quadratic coupling terms. Using Duhamel’s principle, the problem is reduced to the estimate of the product of two Green kernels, representing probability densities of discrete random walks. The total amount of coupling is then determined by the expected number of crossings between two random walks with strictly different average speeds. This provides a discrete analogue of the arguments developed in [3,9] in connection with continuous random processes.展开更多
The authors study a 3 x 3 rate-type viscoelastic system, which is a relaxation approximation to a 2 x 2 quasi-linear hroerbolic system, including the well-known p-system. The nonlinear stability of two-mode shock wave...The authors study a 3 x 3 rate-type viscoelastic system, which is a relaxation approximation to a 2 x 2 quasi-linear hroerbolic system, including the well-known p-system. The nonlinear stability of two-mode shock waves in this relaxation approximation is proved.展开更多
A scheme for switching of the optical bistability(OB) and multi-stability(OM) in a dielectric slab doped with a three-level ladder-configuration n-doped semiconductor quantum well is simulated. It is shown that the bi...A scheme for switching of the optical bistability(OB) and multi-stability(OM) in a dielectric slab doped with a three-level ladder-configuration n-doped semiconductor quantum well is simulated. It is shown that the bistable behavior of the system in dielectric slab can be controlled via amplitude or relative phase of applied fields. This optical system may provide some new possibilities for test the switching process.展开更多
基金National Natural Science Foundation of China under Grant Nos.10472091,10332030,and 10502042
文摘The mean first-passage time of a bistable system with time-delayed feedback driven by multiplicative non-Gaussian noise and additive Gaussian white noise is investigated. Firstly, the non-Markov process is reduced to the Markov process through a path-integral approach; Secondly, the approximate Fokker-Planck equation is obtained by applying the unified coloured noise approximation, the small time delay approximation and the Novikov Theorem. The functional analysis and simplification are employed to obtain the approximate expressions of MFPT. The effects of non-Gaussian parameter （measures deviation from Gaussian character） r, the delay time τ, the noise correlation time to, the intensities D and a of noise on the MFPT are discussed. It is found that the escape time could be reduced by increasing the delay time τ, the noise correlation time τ0, or by reducing the intensities D and α. As far as we know, this is the first time to consider the effect of delay time on the mean first-passage time in the stochastic dynamical system.
基金Project (No. 60574088) supported by the National Natural ScienceFoundation of China
文摘In this paper we propose a two-layer emergent model for scalable swarm system. The first layer describes the indi-vidual flocking behavior to the local goal position (the center of minimal circumcircle decided by the neighbors in the positive visual set of individuals) resulting from the individual motion to one or two farthest neighbors in its positive visual set; the second layer describes the emergent aggregating swarm behavior resulting from the individual motion to its local goal position. The scale of the swarm will not be limited because only local individual information is used for modelling in the two-layer topology. We study the stability properties of the swarm emergent behavior based on Lyapunov stability theory. Simulations showed that the swarm system can converge to goal regions while maintaining cohesiveness.
基金Supported by the Natural Science Foundation of China under Grant No.10865006the Natural Science Foundation of Shaanxi Province under Grant No.2010JQ1014the Science Foundation of Baoji University of Science and Arts of China under Grant No.ZK0954
文摘The asymmetric effects on the escape rates from the stable states x±in the bistable system are analyzed. The results indicate that the multiplicative noise and the additive noise always enhance the particle escape from stable states x±of bistable.However,the asymmetric parameter r enhances the particle escape from stable state x_+,and holds back the particle escape from stable state x_-.
文摘For a long time it was a common opinion that hyperbolic attractors are artificial mathematical constructions. However, in the recent papers there were proposed physically realizable systems that possess, in their phase space, the set with features that are very similar to hyperbolic type of attractors. As is known, invariant sets are called hyperbolic attractors of the dynamical system if they are closed, topologically transitive subsets, and every their trajectory possesses uniform hyperbolicity. Very familiar types of the hyperbolic attractors are Smale-Williams＇ solenoid and Plykin＇s attractor. Further, it is well known that chaotic systems are very sensitive to the external perturbations. This property is used for controlling nonlinear systems and chaos suppression. Thus, an important question arises： Is it possible to suppress chaos in systems with hyperbolic attractors because these attractors are structurally stable subsets？ In the present contribution we study the possibility of stabilization of chaotic oscillations in systems with the Smale-Williams hyperbolic attractors by means of the Pyragas method with a delay. It is shown that by means of external perturbation the dynamical system could be controllable： the hyperbolic attractor degenerates into a periodic one.
基金the European TMR network"Hyperbolic Systems of Conservation Laws"! ERBFMRXCT960033
文摘The authors consider systems of the form where the matrix A(u) is assumed to be strictly hyperbolic and with the property that the integral curves of the eigenvector fields are straight lines. For this class of systems one can define a natural Riemann solver, and hence a Godunov scheme, which generalize the standard Riemann solver and Godunov scheme for conservative systems. This paper shows convergence and L1 stability for this scheme when applied to data with small total variation. The main step in the proof is to estimate the increase in the total variation produced by the scheme due to quadratic coupling terms. Using Duhamel’s principle, the problem is reduced to the estimate of the product of two Green kernels, representing probability densities of discrete random walks. The total amount of coupling is then determined by the expected number of crossings between two random walks with strictly different average speeds. This provides a discrete analogue of the arguments developed in [3,9] in connection with continuous random processes.
文摘The authors study a 3 x 3 rate-type viscoelastic system, which is a relaxation approximation to a 2 x 2 quasi-linear hroerbolic system, including the well-known p-system. The nonlinear stability of two-mode shock waves in this relaxation approximation is proved.
文摘A scheme for switching of the optical bistability(OB) and multi-stability(OM) in a dielectric slab doped with a three-level ladder-configuration n-doped semiconductor quantum well is simulated. It is shown that the bistable behavior of the system in dielectric slab can be controlled via amplitude or relative phase of applied fields. This optical system may provide some new possibilities for test the switching process.
