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Variable-time impulsive control for bipartite synchronization of coupled complex networks with signed graphs

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  • Yang, Shiju
  • Li, Chuandong
  • He, Xiping
  • Zhang, Wanli

Abstract

This paper investigates the bipartite synchronization of coupled complex networks (CCNs) with signed graphs via variable-time impulsive (VTI) control. Different from the traditional complex networks, the communication topology between nodes of the complex networks can be either collaborative or antagonistic. In addition, the appearance of impulses is always dependent on each node in the network instead of appearing at fixed instants. Furthermore, by utilizing the B-equivalent technique, the VTI network models can be changed as fixed-time impulsive CCNs. The fixed-time impulsively controlled CCNs can be regarded as the comparison systems of the signed CCNs with variable-time impulses. By 1-norm analytical techniques, several assumptions are derived to guarantee every solution of the coupled error nodes intersect each discontinuous impulsive surface exactly once. Some sufficient conditions with theoretical demonstration are presented to guarantee the bipartite synchronization under mathematical induction. Simulation results are carried out to show the effectiveness of the obtained results.

Suggested Citation

  • Yang, Shiju & Li, Chuandong & He, Xiping & Zhang, Wanli, 2022. "Variable-time impulsive control for bipartite synchronization of coupled complex networks with signed graphs," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    • Handle: RePEc:eee:apmaco:v:420:y:2022:i:c:s0096300321009826
    DOI: 10.1016/j.amc.2021.126899
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    References listed on IDEAS

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    1. Zhang, Wanli & Yang, Xinsong & Yang, Shiju & Alsaedi, Ahmed, 2021. "Finite-time and fixed-time bipartite synchronization of complex networks with signed graphs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 319-329.
    2. Duncan J. Watts & Steven H. Strogatz, 1998. "Collective dynamics of ‘small-world’ networks," Nature, Nature, vol. 393(6684), pages 440-442, June.
    3. Guo, Xing & Lu, Jianquan & Alsaedi, Ahmed & Alsaadi, Fuad E., 2018. "Bipartite consensus for multi-agent systems with antagonistic interactions and communication delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 488-497.
    4. Dahui, Wang & Li, Zhou & Zengru, Di, 2006. "Bipartite producer–consumer networks and the size distribution of firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 359-366.
    5. Yang, Xujun & Li, Chuandong & Huang, Tingwen & Song, Qiankun, 2017. "Mittag–Leffler stability analysis of nonlinear fractional-order systems with impulses," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 416-422.
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    Cited by:

    1. Huan, Mingchen & Li, Chuandong, 2023. "Synchronization of reaction–diffusion neural networks with sampled-data control via a new two-sided looped-functional," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Xu, Ziqiang & Li, Yun & Zhan, Xisheng & Yan, Huaicheng & Han, Yiyan, 2024. "Time-varying formation of uncertain nonlinear multi-agent systems via adaptive feedback control approach with event-triggered impulsive estimator," Applied Mathematics and Computation, Elsevier, vol. 475(C).
    3. Cheng Zhang & Chuan Zhang & Fanwei Meng & Yi Liang, 2023. "Event-Triggered Control for Intra/Inter-Layer Synchronization and Quasi-Synchronization in Two-Layer Coupled Networks," Mathematics, MDPI, vol. 11(6), pages 1-15, March.
    4. Shi, Sangli & Wang, Zhengxin & Song, Qiang & Xiao, Min & Jiang, Guo-Ping, 2022. "Leader-following quasi-bipartite synchronization of coupled heterogeneous harmonic oscillators via event-triggered control," Applied Mathematics and Computation, Elsevier, vol. 427(C).

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