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Cluster synchronization for directed community networks via pinning partial schemes

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  • Hu, Cheng
  • Jiang, Haijun

Abstract

In this paper, we focus on driving a class of directed networks to achieve cluster synchronization by pinning schemes. The desired cluster synchronization states are no longer decoupled orbits but a set of un-decoupled trajectories. Each community is considered as a whole and the synchronization criteria are derived based on the information of communities. Several pinning schemes including feedback control and adaptive strategy are proposed to select controlled communities by analyzing the information of each community such as indegrees and outdegrees. In all, this paper answers several challenging problems in pinning control of directed community networks: (1) What communities should be chosen as controlled candidates? (2) How many communities are needed to be controlled? (3) How large should the control gains be used in a given community network to achieve cluster synchronization? Finally, an example with numerical simulations is given to demonstrate the effectiveness of the theoretical results.

Suggested Citation

  • Hu, Cheng & Jiang, Haijun, 2012. "Cluster synchronization for directed community networks via pinning partial schemes," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1368-1377.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:11:p:1368-1377
    DOI: 10.1016/j.chaos.2012.06.015
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    References listed on IDEAS

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    1. W. L. Lu & B. Liu & T. Chen, 2010. "Cluster synchronization in networks of distinct groups of maps," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 77(2), pages 257-264, September.
    2. Liu, Meng & Shao, Yingying & Fu, Xinchu, 2009. "Complete synchronization on multi-layer center dynamical networks," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2584-2591.
    3. Gu, Ya-Qin & Shao, Chun & Fu, Xin-Chu, 2006. "Complete synchronization and stability of star-shaped complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 480-488.
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    Cited by:

    1. Wu, Jianshe & Zhang, Long & Li, Yong & Jiao, Yang, 2016. "Partition signed social networks via clustering dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 568-582.
    2. Ding, Dawei & Yan, Jie & Wang, Nian & Liang, Dong, 2017. "Pinning synchronization of fractional order complex-variable dynamical networks with time-varying coupling," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 41-50.
    3. Hu, Aihua & Cao, Jinde & Hu, Manfeng & Guo, Liuxiao, 2015. "Cluster synchronization of complex networks via event-triggered strategy under stochastic sampling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 99-110.

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