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Cluster synchronization for directed heterogeneous dynamical networks via decentralized adaptive intermittent pinning control

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Abstract

In this paper, by proposing a novel adaptive intermittent scheme, we consider the intermittent pinning-control problem for cluster synchronization of directed heterogeneous dynamical networks, i.e., directed networks with nonidentical dynamical nodes. Through constructing a piecewise Lyapunov function and utilizing the analysis technique, some sufficient conditions to guarantee global cluster synchronization are derived. It is noted that the adaptive intermittent strategy developed in this paper is decentralized, which only relies on some local information rather than the global information of the whole network. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.

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Acknowledgments

The authors are grateful to the editor and anonymous reviewers for their constructive comments and suggestions that helped to improve the content as well as the quality of the paper.

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Authors and Affiliations

  1. Faculty of Science, Jiangsu University, Zhenjiang, 212013, Jiangsu, China

    Shuiming Cai & Qiang Jia

  2. Institute of Systems Biology, Shanghai University, Shanghai, 200444, China

    Zengrong Liu

Authors
  1. Shuiming Cai
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  2. Qiang Jia
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  3. Zengrong Liu
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Corresponding author

Correspondence to Shuiming Cai.

Additional information

This work was supported by the National Science Foundation of China (Grant Nos. 11402100 and 11331009), National Science Foundation of China, Tian Yuan Special Foundation (Grant No. 11326193), Natural Science Foundation of Jiangsu Province (Grant No. BK20130535), and the Research Foundation for Advanced Talents of Jiangsu University (13JDG027).

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Cai, S., Jia, Q. & Liu, Z. Cluster synchronization for directed heterogeneous dynamical networks via decentralized adaptive intermittent pinning control. Nonlinear Dyn 82, 689–702 (2015). https://doi.org/10.1007/s11071-015-2187-x

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  • DOI: https://doi.org/10.1007/s11071-015-2187-x

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