Pinning and impulsive synchronization control of complex dynamical networks with non-derivative and derivative coupling

In this paper, the problem of pinning and impulsive synchronization between two complex dynamical networks with non-derivative and derivative coupling is investigated. A hybrid controller, which contains a pinning controller and a pinning impulsive controller, is proposed simultaneously. Based on the Lyapunov stability theory and mathematical analysis technique, some novel criteria of synchronization are derived, which can guarantee that the response network asymptotically synchronizes to the drive network by combining pinning control and pinning impulsive control. Moreover, the restrictions about non-derivative coupling matrix, impulsive intervals and the number of pinned nodes are removed. Numerical examples are presented finally to illustrate the effectiveness of the theoretical results.