Pinning control of complex networks with time-varying inner and outer coupling

This paper addresses the pinning synchronization of nonlinear multiple time-varying coupling complex networks. Time-varying inner coupling in the single node state space and time-varying outer coupling among nodes in an entire complex network are taken into consideration. The main contribution is to propose some pinning synchronization criterion by which time-varying complex networks can be synchronized to the desired state. Besides, different parameters of linear controllers, adaptive controllers and adaptive coupling strength on the synchronization have been investigated. It is found that complex networks can achieve global synchronization by adaptively adjusting the coupling strength or controllers. Finally, simulation examples of random networks are given to verify the theoretical results.