An efficient approach to synchronization of complex networks with different dynamical structures

This paper is concerned with carrying out synchronization between two completely different complex dynamical networks, which is called generalized outer synchronization. Our objective is to develop a control scheme so as to achieve this generalized outer synchronization. The derived result is built upon Barbalat´s Lemma. It is shown that when two complex dynamical networks to be synchronized have different topologies and diverse node dynamics, the designed controller is a nonlinear one. In particular, when two complex dynamical networks have the same topological structures or identical dynamics, the designed controller can be simplified, sometimes to a linear controller. Computer simulations are presented to show that generalized outer synchronization can be quickly realized under the designed controller.