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Cluster synchronization in a network of nonlinear systems with directed topology and competitive relationships

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  • Wang, Xin
  • Zhai, Shidong
  • Luo, Guoqiang
  • Huang, Tao

Abstract

This article studies the cluster synchronization problem of coupled nonlinear systems with directed topology and competitive relationships. We assume that nodes within the same cluster have the same intrinsic dynamics, while the dynamics of nodes belonging to different clusters are different. In the same cluster, there only exist cooperative relationships, and there may have competitive relationships among nodes belonging to different clusters. Under the assumptions that the dynamic of each node satisfies one-sided Lipschitz condition, the digraph of each cluster is strongly connected, and the digraph between different clusters satisfies the cluster-input-equivalence condition, some sufficient conditions for cluster synchronization in the cases of linear coupling and nonlinear coupling are obtained respectively. The obtained conditions are presented as some algebraic conditions which are easy to solve. Finally, the obtained results are validated by two numerical simulations.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:421:y:2022:i:c:s0096300322000170
    DOI: 10.1016/j.amc.2022.126931
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    References listed on IDEAS

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    4. Cai, Yuliang & Zhang, Huaguang & Liu, Yang & He, Qiang, 2020. "Distributed bipartite finite-time event-triggered output consensus for heterogeneous linear multi-agent systems under directed signed communication topology," Applied Mathematics and Computation, Elsevier, vol. 378(C).
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