Global adaptive synchronization of complex networks with nonlinear delay coupling interconnections

This Letter is dealt with global synchronization problem of a class of complex network systems with the time delay nonlinear coupling via adaptive methodology. The nonlinear functions and the delay coupling interconnections considered here are in a high-order polynomial form, which is less restrictive than the cases addressed in the literature. An adaptive controller is presented and it is shown by the Lyapunov method that the resulting synchronization error of the adaptive system is asymptotically stable. A numerical example is given to illustrate the effectiveness of the proposed controller.