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

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.

Automated summary

This paper investigates the global synchronization of complex networks with fractional-order chaotic nodes. A simple Lyapunov function and a feedback controller are used. The authors propose the GMMP method to obtain numerical solutions and new synchronous criteria based on feedback control. Numerical simulations demonstrate the effectiveness and universality of the proposed method.