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Edge-Based Synchronization Control Criteria of Complex Dynamical Networks with Reaction–Diffusions

Author

Listed:
  • Tao Xie

    (School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
    Huangshi Key Laboratory of Metaverse and Virtual Simulation, School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China)

  • Qike Zhang

    (School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
    Huangshi Key Laboratory of Metaverse and Virtual Simulation, School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China)

  • Xing Xiong

    (School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
    Huangshi Key Laboratory of Metaverse and Virtual Simulation, School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China)

Abstract

This research investigates the edge-based asymptotic synchronization of delayed complex dynamical networks with reaction–diffusions and by an edge-based adaptive pinning control technique. Sufficient conditions for reaction–diffusion networks to realize synchronization are provided by Green’s formula, Wirtinger inequality, inequality analysis techniques, and contradiction methods. The results show that network synchronization can be achieved by pinning any edge of the network (the choice of edge is arbitrary), which greatly reduces the difficulty of control. Lastly, a series of numerical examples illustrating the theoretical findings is provided.

Suggested Citation

  • Tao Xie & Qike Zhang & Xing Xiong, 2024. "Edge-Based Synchronization Control Criteria of Complex Dynamical Networks with Reaction–Diffusions," Mathematics, MDPI, vol. 12(12), pages 1-18, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1911-:d:1418867
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    References listed on IDEAS

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    1. Hu, Jingting & Sui, Guixia & Li, Xiaodi, 2020. "Fixed-time synchronization of complex networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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