Adaptive outer synchronization and topology identification between two complex dynamical networks with time-varying delay and disturbance

In this paper, we investigate adaptive outer synchronization for identifying unknown network topology and parameters between two coupled complex networks with time-varying delays existing in the node dynamics and coupling forms. By designing adaptive controllers and updating laws, we obtain two theorems on the appearance of outer synchronization using Lyapunov stability theory. In the numerical examples, we provide the detailed identification criteria of network topology and system parameter according to the obtained theorems and give some numerical examples to show the efficiency of the proposed controllers.