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Cluster synchronization of overlapping uncertain complex networks with time-varying impulse disturbances

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Abstract

This paper addresses the scheme of cluster synchronization of overlapping uncertain complex networks with time-varying impulse disturbances. Many existing works on cluster synchronization focus on synchronizing and desynchronizing impulses separately, but the effects of two types of impulses are rarely observed. Here, we present the analysis of the two types (time-varying impulses) in complex networks. Furthermore, by means of stochastic stability theorem, sufficient conditions for guaranteeing the realization of cluster synchronization are derived. The network topology is assumed to be overlapping community, which includes an overlapping sub community with different dynamic behavior due to its identity (community). Finally, numerical examples are exploited to verify the correctness and effectiveness of theoretical results.

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Acknowledgments

The authors are grateful to the anonymous reviews and editors for their valuable comments and suggestions that have helped to improve the presentation of this paper. This work was supported by the National Nature Science foundation of China (Nos 51276081, 71073072), the Society Science Foundation from Ministry of Education of China (Nos 12YJAZH002, 08JA790057), the Project Funded by The Priority Academic Program Development of Jiangsu Higher Education Institutions, the Advanced Talents’ Foundation of Jiangsu University (Nos 07JDG054, 10JDG140) and the Students’ Research Foundation of Jiangsu University (No Y13A127 and 12A415).

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  1. Nonlinear Scientific Research Center, Jiangsu University, Zhenjiang, 212013, Jiangsu, People’s Republic of China

    Guoliang Cai, Shengqin Jiang, Shuiming Cai & Lixin Tian

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  1. Guoliang Cai
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  2. Shengqin Jiang
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  3. Shuiming Cai
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  4. Lixin Tian
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Correspondence to Shengqin Jiang.

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Cai, G., Jiang, S., Cai, S. et al. Cluster synchronization of overlapping uncertain complex networks with time-varying impulse disturbances. Nonlinear Dyn 80, 503–513 (2015). https://doi.org/10.1007/s11071-014-1884-1

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  • DOI: https://doi.org/10.1007/s11071-014-1884-1

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