Synchronization of a complex dynamical network with free coupling matrix

This paper considers synchronization problem of a complex dynamical network. For the problem, the virtual target node is chosen as one of nodes in the complex network and only one connection is needed between an isolate target node and virtual target node not any more connections. Moreover, our synchronization scheme does not need additional conditions and information of coupling matrix comparing with existing works. Based on Lyapunov stability theory, a design criterion for a novel adaptive feedback controller for the synchronization between the isolate target node and another nodes of the complex network is proposed. Finally, the proposed method is applied to a numerical example in order to show the effectiveness of our results.