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On pinning synchronisability of complex networks with arbitrary topological structure

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  • Jiahu Qin
  • Wei Zheng
  • Huijun Gao

Abstract

This article aims to investigate the pinning synchronisability of complex networks under arbitrary topological structures with a focus on the case with directed graph topology. More specifically, we explore the necessary and sufficient conditions on choosing the pinned nodes to guarantee the pinning synchronisability of complex networks. It is found that the pinning synchronisability of complex networks relies totally on the way to pin the nodes as long as the coupling strength is large enough. Furthermore, it is proven that the entire network can synchronise exponentially fast. The least synchronisation speed can be specified as well. Finally, based on the theoretical findings proposed in this article, we provide the specific procedures for finding a least number of pinned nodes to realise the pinning synchronisability of complex networks.

Suggested Citation

  • Jiahu Qin & Wei Zheng & Huijun Gao, 2011. "On pinning synchronisability of complex networks with arbitrary topological structure," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(9), pages 1559-1571.
    • Handle: RePEc:taf:tsysxx:v:42:y:2011:i:9:p:1559-1571
    DOI: 10.1080/00207721.2011.555014
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    Cited by:

    1. Wang, Xin & Zhai, Shidong & Luo, Guoqiang & Huang, Tao, 2022. "Cluster synchronization in a network of nonlinear systems with directed topology and competitive relationships," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    2. Zhai, Shidong & Huang, Tao & Luo, Guoqiang & Wang, Xin & Ma, Jun, 2022. "Pinning bipartite synchronization for coupled nonlinear systems with antagonistic interactions and time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).

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