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Cluster synchronization in directed networks of non-identical systems with noises via random pinning control

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  • Hu, Aihua
  • Cao, Jinde
  • Hu, Manfeng
  • Guo, Liuxiao

Abstract

This paper is concerned with the issue of mean square cluster synchronization in directed networks, which consist of non-identical nodes infected by communication noises. The pinning control method is employed in designing controllers for guaranteeing cluster synchronization, meanwhile, all the controllers are supposed to occur with different probabilities by introducing the Bernoulli stochastic variables. Based on the Lyapunov stability theory and the stochastic theory, the sufficient synchronization conditions are derived and proved theoretically, which are mainly for the controllers to be designed and the noise intensities. Finally, some numerical examples are presented to demonstrate the effectiveness of the results.

Suggested Citation

  • Hu, Aihua & Cao, Jinde & Hu, Manfeng & Guo, Liuxiao, 2014. "Cluster synchronization in directed networks of non-identical systems with noises via random pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 537-548.
  • Handle: RePEc:eee:phsmap:v:395:y:2014:i:c:p:537-548
    DOI: 10.1016/j.physa.2013.10.040
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    References listed on IDEAS

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    1. Yang-Yu Liu & Jean-Jacques Slotine & Albert-László Barabási, 2011. "Controllability of complex networks," Nature, Nature, vol. 473(7346), pages 167-173, May.
    2. Pagani, Giuliano Andrea & Aiello, Marco, 2013. "The Power Grid as a complex network: A survey," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(11), pages 2688-2700.
    3. Le Yu & Lilan Tu & Hongfang Liu, 2013. "Adaptive cluster synchronization for a complex dynamical network with delays and stochastic perturbation," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(4), pages 1-6, April.
    4. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    5. Liu, Xiwei & Chen, Tianping, 2008. "Synchronization analysis for nonlinearly-coupled complex networks with an asymmetrical coupling matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(16), pages 4429-4439.
    6. Wu, Jianshe & Wang, Xiaohua & Jiao, Licheng, 2012. "Synchronization on overlapping community network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 508-514.
    7. Singh, Aradhana & Jalan, Sarika, 2012. "Transition from the self-organized to the driven dynamical clusters," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6655-6663.
    8. Tauro, Carolina B. & Tamarit, Francisco A. & Gleiser, Pablo M., 2012. "Synchronization in lattice-embedded scale-free networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 834-842.
    9. Tang, Jinjun & Wang, Yinhai & Liu, Fang, 2013. "Characterizing traffic time series based on complex network theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 4192-4201.
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    Citations

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    Cited by:

    1. Zhou, Jiaying & Zhao, Yi & Wu, ZhaoYan, 2019. "Cluster synchronization of fractional-order directed networks via intermittent pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 519(C), pages 22-33.
    2. Fu, Chenbo & Wang, Jinbao & Xiang, Yun & Wu, Zhefu & Yu, Li & Xuan, Qi, 2017. "Pinning control of clustered complex networks with different size," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 184-192.
    3. Jianbao Zhang & Yi Wang & Zhongjun Ma & Jianlong Qiu & Fawaz Alsaadi, 2018. "Intermittent Control for Cluster-Delay Synchronization in Directed Networks," Complexity, Hindawi, vol. 2018, pages 1-9, February.
    4. Bin Yang & Xin Wang & Jian-an Fang & Yuhua Xu, 2019. "The Impact of Coupling Function on Finite-Time Synchronization Dynamics of Multi-Weighted Complex Networks with Switching Topology," Complexity, Hindawi, vol. 2019, pages 1-15, March.
    5. 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.
    6. Gequn, Liu & Zhiguo, Zhan & Knowles, Gareth, 2015. "Design of inner coupling matrix for robustly self-synchronizing networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 440(C), pages 68-80.
    7. Feng, Jianwen & Yang, Pan & Zhao, Yi, 2016. "Cluster synchronization for nonlinearly time-varying delayed coupling complex networks with stochastic perturbation via periodically intermittent pinning control," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 52-68.
    8. Wang, Fei & Yang, Yongqing & Hu, Manfeng & Xu, Xianyun, 2015. "Projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 134-143.
    9. Cai, Shuiming & Zhou, Feilong & He, Qinbin, 2019. "Fixed-time cluster lag synchronization in directed heterogeneous community networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 128-142.

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