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

Yifan Zhang, Tianzeng Li, Zhiming Zhang and Yu Wang
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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

Mathematics, 2022, vol. 10, issue 11, 1-22

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.

Keywords: Lyapunov function; fractional-order; synchronization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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