The existence of generalized synchronisation of three bidirectionally coupled chaotic systems

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

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.

Keywords: generalised synchronisation manifold compression fixed point exponential attractive property

Received: 18 February 2009
Revised: 05 August 2009
Accepted manuscript online:

PACS:	05.45.Xt	(Synchronization; coupled oscillators)
	05.45.Pq	(Numerical simulations of chaotic systems)

Fund: 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.

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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 2010 Chin. Phys. B 19 020511

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[1]	Hölder continuity of two types of bidirectionally coupled generalised synchronisation manifold Guo Liu-Xiao(过榴晓), Xu Zhen-Yuan(徐振源), and Hu Ai-Hua(胡爱花) . Chin. Phys. B, 2011, 20(1): 010507.

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The existence of generalized synchronisation of three bidirectionally coupled chaotic systems

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