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.