The existence of generalized synchronisation of three bidirectionally coupled chaotic systems

doi:10.1088/1674-1056/19/2/020511

中国物理B ›› 2010, Vol. 19 ›› Issue (2): 20511-020511.doi: 10.1088/1674-1056/19/2/020511

The existence of generalized synchronisation of three bidirectionally coupled chaotic systems

徐振源¹, 过榴晓¹, 胡爱花²

(1)School of Science, Jiangnan University, Wuxi 214122, China; (2)School of Science, Jiangnan University, Wuxi 214122, China;School of Information Technology, Jiangnan University, Wuxi 214122, China

收稿日期:2009-02-18 修回日期:2009-08-05 出版日期:2010-02-15 发布日期:2010-02-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 60575038), the Youth Foundation of Jiangnan University (Grant No. 314000-52210756) and the Program for Innovative Research Team of Jiangnan University.

The existence of generalized synchronisation of three bidirectionally coupled chaotic systems

Hu Ai-Hua(胡爱花)^a)b)^†, Xu Zhen-Yuan(徐振源)^a), and Guo Liu-Xiao(过榴晓)^a)

^a School of Science, Jiangnan University, Wuxi 214122, China; ^b School of Information Technology, Jiangnan University, Wuxi 214122, China

Received:2009-02-18 Revised:2009-08-05 Online:2010-02-15 Published:2010-02-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 60575038), the Youth Foundation of Jiangnan University (Grant No. 314000-52210756) and the Program for Innovative Research Team of Jiangnan University.

摘要/Abstract

摘要： The existence of two types of generalized synchronisation is studied. The model considered here includes three bidirectionally coupled chaotic systems, and two of them denote the driving systems, while the rest stands for the response system. Under certain conditions, the existence of generalised synchronisation can be turned to a problem of compression fixed point in the family of Lipschitz functions. In addition, theoretical proofs are proposed to the exponential attractive property of generalised synchronisation manifold. Numerical simulations validate the theory.

Abstract: The existence of two types of generalized synchronisation is studied. The model considered here includes three bidirectionally coupled chaotic systems, and two of them denote the driving systems, while the rest stands for the response system. Under certain conditions, the existence of generalised synchronisation can be turned to a problem of compression fixed point in the family of Lipschitz functions. In addition, theoretical proofs are proposed to the exponential attractive property of generalised synchronisation manifold. Numerical simulations validate the theory.

Key words: generalised synchronisation manifold, compression fixed point, exponential attractive property

中图分类号: (Synchronization; coupled oscillators)

05.45.Xt

05.45.Pq (Numerical simulations of chaotic systems)

胡爱花, 徐振源, 过榴晓. The existence of generalized synchronisation of three bidirectionally coupled chaotic systems[J]. 中国物理B, 2010, 19(2): 20511-020511.

Hu Ai-Hua(胡爱花), Xu Zhen-Yuan(徐振源), and Guo Liu-Xiao(过榴晓). The existence of generalized synchronisation of three bidirectionally coupled chaotic systems[J]. Chin. Phys. B, 2010, 19(2): 20511-020511.

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