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Cluster synchronization analysis of complex dynamical networks by input-to-state stability

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Abstract

Cluster synchronization is an interesting issue in complex dynamical networks with community structure. In this paper, we study cluster synchronization of complex networks with non-identical systems by input-to-state stability. Some sufficient conditions that ensure cluster synchronization of complex networks are provided. We show that the cluster synchronization is difficult to achieve if there are some links among different clusters. The analysis is then extended to the case where the outer coupling strengths are adaptive. Finally, numerical simulations are given to validate our theoretical analysis.

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Acknowledgements

This work was jointly supported by Région Haute-Normandie France and FEDER-RISC, the National Natural Science Foundation of China under Grant Nos. 11172215, 11071280, 50739003, the Youth Project of Hubei Education Department under Grant Nos. Q20111607, Q20111611, and the Foundation of Wuhan Textile University under Grant No. 113073. The authors wish to thank the reviewers and editor for their valuable comments and suggestions.

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Authors and Affiliations

  1. College of Mathematica and Computer Science, Wuhan Textile University, Wuhan, 430073, China

    Junchan Zhao

  2. Applied Mathematics Laboratory, University of Le Havre, 76058, Le Havre Cedex, France

    Junchan Zhao & M. A. Aziz-Alaoui

  3. LITIS, University of Le Havre, 76058, Le Havre Cedex, France

    Cyrille Bertelle

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  1. Junchan Zhao
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  2. M. A. Aziz-Alaoui
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  3. Cyrille Bertelle
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Correspondence to Junchan Zhao.

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Zhao, J., Aziz-Alaoui, M.A. & Bertelle, C. Cluster synchronization analysis of complex dynamical networks by input-to-state stability. Nonlinear Dyn 70, 1107–1115 (2012). https://doi.org/10.1007/s11071-012-0516-x

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  • DOI: https://doi.org/10.1007/s11071-012-0516-x

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