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Adaptive exponential cluster synchronization in colored community networks via aperiodically intermittent pinning control

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Abstract

This paper investigates the problem of pinning cluster synchronization for colored community networks via adaptive aperiodically intermittent control. Firstly, a general colored community network model is proposed, where the isolated nodes can interact through different kinds of connections in different communities and the interactions between different pair of communities can also be different, and moreover, the nodes in different communities can have different state dimensions. Then, an adaptive aperiodically intermittent control strategy combined with pinning scheme is developed to realize cluster synchronization of such colored community network. By introducing a novel piecewise continuous auxiliary function, some globally exponential cluster synchronization criteria are rigorously derived according to Lyapunov stability theory and piecewise analysis approach. Based on the derived criteria, a guideline to illustrate which nodes in each community should be preferentially pinned is given. It is noted that the adaptive intermittent pinning control is aperiodic, in which both control width and control period are allowed to be variable. Finally, a numerical example is provided to show the effectiveness of the theoretical results obtained.

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Acknowledgements

The authors thank the editor and anonymous reviewers for their valuable comments and suggestions which have helped to improve the quality of the paper.

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Authors and Affiliations

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

    Peipei Zhou & Shuiming Cai

  2. Department of Mathematics, Xuchang University, Xuchang, 461000, China

    Jianwei Shen

  3. Department of Mathematics, Yunnan Normal University, Kunming, 650092, PR China

    Zengrong Liu

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  1. Peipei Zhou
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  2. Shuiming Cai
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  3. Jianwei Shen
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  4. 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 11572278) and Young Core Teachers Training Project of Jiangsu University.

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Zhou, P., Cai, S., Shen, J. et al. Adaptive exponential cluster synchronization in colored community networks via aperiodically intermittent pinning control. Nonlinear Dyn 92, 905–921 (2018). https://doi.org/10.1007/s11071-018-4099-z

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