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Chin. Phys. B, 2011, Vol. 20(1): 010507    DOI: 10.1088/1674-1056/20/1/010507
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Hölder continuity of two types of bidirectionally coupled generalised synchronisation manifold

Guo Liu-Xiao(过榴晓)a)b), Xu Zhen-Yuan(徐振源)a),and Hu Ai-Hua(胡爱花)a)b)
a School of Science, Jiangnan University, Wuxi 214122, China; b School of Information Technology, Jiangnan University, Wuxi 214122, China
Abstract  This paper studies the existence of Höolder continuity of bidirectionally coupled generalised synchronisation (GS). Based on the slaving principle of synergetics and the modified system approach, it classifies the GS into several types. The existences of two main types of Hölder continuous bidirectionally coupled GS inertial manifolds are theoretically analysed and proved by using the Schauder fixed point theorem. Numerical simulations illustrate the theoretical results.
Keywords:  bidirectionally coupled      generalised synchronisation manifold      Schauder fixed point theorem      Hölder continuity  
Received:  10 August 2009      Revised:  08 August 2010      Accepted manuscript online: 
PACS:  05.45.Gg (Control of chaos, applications of chaos)  
  05.45.Xt (Synchronization; coupled oscillators)  
Fund: Project supported by the National Natural Science Foundation of China (Grants Nos. 11002061 and 10901073) and the Fundamental Research Funds for the Central Universities, China (Grant No. JUSRP10912).

Cite this article: 

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

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