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Novel Methods for the Global Synchronization of the Complex Dynamical Networks with Fractional-Order Chaotic Nodes

Author

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  • Yifan Zhang

    (School of Energy and Intelligence Engineering, Henan University of Animal Husbandry and Economy, Zhengzhou 450011, China)

  • Tianzeng Li

    (College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China)

  • Zhiming Zhang

    (School of Energy and Intelligence Engineering, Henan University of Animal Husbandry and Economy, Zhengzhou 450011, China)

  • Yu Wang

    (College of Mathematics and Statistics, Sichuan University of Science and Engineering, Zigong 643000, China)

Abstract

The global synchronization of complex networks with fractional-order chaotic nodes is investigated via a simple Lyapunov function and the feedback controller in this paper. Firstly, the GMMP method is proposed to obtain the numerical solution of the fractional-order nonlinear equation based on the relation of the fractional derivatives. Then, the new feedback controllers are proposed to achieve synchronization between the complex networks with the fractional-order chaotic nodes based on feedback control. We propose some new sufficient synchronous criteria based on the Lyapunov stability and a simple Lyapunov function. By the numerical simulations of the complex networks, we find that these synchronous criteria can apply to the arbitrary complex dynamical networks with arbitrary fractional-order chaotic nodes. Numerical simulations of synchronization between two complex dynamical networks with the fractional-order chaotic nodes are given by the GMMP method and the Newton method, and the results of numerical simulation demonstrate that the proposed method is universal and effective.

Suggested Citation

  • Yifan Zhang & Tianzeng Li & Zhiming Zhang & Yu Wang, 2022. "Novel Methods for the Global Synchronization of the Complex Dynamical Networks with Fractional-Order Chaotic Nodes," Mathematics, MDPI, vol. 10(11), pages 1-22, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1928-:d:831522
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    References listed on IDEAS

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