Synchronization Between Two Complex Dynamical Networks Using Scalar Signals Under Pinning Control

In this paper, a new scheme for synchronization between two or more complex networks is proposed using scalar signals under pinning control. Unlike common synchronization schemes, where all states of the driving networks are transmitted to the response network and all the nodes in the response network are required to be controlled, here, it is suggested that only a few nodes in the response network are controlled and only a few scalar signals are required to be transmitted from the driving network to the response one. Some criteria for synchronization between two or more complex dynamical networks are given in the form of linear matrix inequality. Furthermore, how to choose the pinned nodes according to the network topology is discussed by a numerical simulation method. Some typical network configurations are simulated, and the simulation results show that the proposed synchronization scheme is effective for the synchronization between two or more complex networks.