Synchronization of fractional order complex dynamical networks

• We proposed a fractional order controller and a synchronization law for fractional order complex networks.
• Some new sufficient synchronization criteria are proposed.
• These criteria can apply to an arbitrary fractional order complex network.

In this letter the synchronization of complex dynamical networks with fractional order chaotic nodes is studied. A fractional order controller for synchronization of complex network is presented. Some new sufficient synchronization criteria are proposed based on the Lyapunov stability theory and the LaSalle invariance principle. These synchronization criteria can apply to an arbitrary fractional order complex network in which the coupling-configuration matrix and the inner-coupling matrix are not assumed to be symmetric or irreducible. It means that this method is more general and effective. Numerical simulations of two fractional order complex networks demonstrate the universality and the effectiveness of the proposed method.