Outer synchronization between two complex networks with identical and nonidentical topological structures

This paper investigates out synchronization with identical topologies connection and the adaptive synchronization with nonidentical topologies connection between two nonlinearly delay-coupled complex networks with the bidirectional actions. A new Lyapunov-Krasovskii functional is constructed for the two complex networks, and the S-procedure is employed to handle the nonlinearities and identical topologies networks. Based on LaSalle invariance principle, combining the nonlinear adaptive controllers and update laws, some criteria are derived to ensure the synchronization between two complex networks with nonidentical topologies. Finally, a numerical example and its simulations are given to illustrate the efficiency of the derived result.