Generalized synchronization of two unidirectionally coupled discrete stochastic dynamical systems

doi:10.1088/1674-1056/20/7/070503

中国物理B ›› 2011, Vol. 20 ›› Issue (7): 70503-070503.doi: 10.1088/1674-1056/20/7/070503

Generalized synchronization of two unidirectionally coupled discrete stochastic dynamical systems

袁志玲, 徐振源, 过榴晓

School of science, Jiangnan University, wuxi 214122, China

收稿日期:2010-09-06 修回日期:2011-03-21 出版日期:2011-07-15 发布日期:2011-07-15

Generalized synchronization of two unidirectionally coupled discrete stochastic dynamical systems

Yuan Zhi-Ling(袁志玲)^†, Xu Zhen-Yuan(徐振源), and Guo Liu-Xiao(过榴晓)

School of science, Jiangnan University, wuxi 214122, China

Received:2010-09-06 Revised:2011-03-21 Online:2011-07-15 Published:2011-07-15

摘要/Abstract

摘要： The existence of two kinds of generalized synchronization manifold in two unidirectionally coupled discrete stochastic dynamical systems is studied in this paper. When the drive system is chaotic and the modified response system collapses to an asymptotically stable equilibrium or asymptotically stable periodic orbit, under certain conditions, the existence of the generalized synchronization can be converted to the problem of a Lipschitz contractive fixed point or Schauder fixed point. Moreover, the exponential attractive property of generalized synchronization manifold is strictly proved. In addition, numerical simulations demonstrate the correctness of the present theory. The physical background and meaning of the results obtained in this paper are also discussed.%vspace1mm

关键词: generalized synchronization manifold, discrete stochastic dynamical system, Lipschitz smoothness, Hö, lder continuity

Abstract: The existence of two kinds of generalized synchronization manifold in two unidirectionally coupled discrete stochastic dynamical systems is studied in this paper. When the drive system is chaotic and the modified response system collapses to an asymptotically stable equilibrium or asymptotically stable periodic orbit, under certain conditions, the existence of the generalized synchronization can be converted to the problem of a Lipschitz contractive fixed point or Schauder fixed point. Moreover, the exponential attractive property of generalized synchronization manifold is strictly proved. In addition, numerical simulations demonstrate the correctness of the present theory. The physical background and meaning of the results obtained in this paper are also discussed.

Key words: generalized synchronization manifold, discrete stochastic dynamical system, Lipschitz smoothness, H?lder continuity

中图分类号: (Synchronization; coupled oscillators)

05.45.Xt

袁志玲, 徐振源, 过榴晓. Generalized synchronization of two unidirectionally coupled discrete stochastic dynamical systems[J]. 中国物理B, 2011, 20(7): 70503-070503.

Yuan Zhi-Ling(袁志玲), Xu Zhen-Yuan(徐振源), and Guo Liu-Xiao(过榴晓) . Generalized synchronization of two unidirectionally coupled discrete stochastic dynamical systems[J]. Chin. Phys. B, 2011, 20(7): 70503-070503.

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Generalized synchronization of two unidirectionally coupled discrete stochastic dynamical systems

Generalized synchronization of two unidirectionally coupled discrete stochastic dynamical systems

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