Outer synchronization of drive-response dynamical networks via adaptive impulsive pinning control

In this paper, outer synchronization between drive and response networks via adaptive impulsive pinning control is investigated. In the pinning control scheme, the controlled nodes are changed adaptively according to the synchronization errors at different impulsive instants. Based on the Lyapunov function method and mathematical analysis, a synchronization criterion is precisely derived. Under this criterion, the impulsive intervals for achieving outer synchronization of two given networks are estimated. Further, an adaptive strategy is designed for a node-to-node pinning impulsive controller, with a corresponding synchronization condition derived. In the proposed adaptive control scheme, the impulsive instants adjust themselves to the needed values as time goes on, and an algorithm for determining the impulsive instants is developed and evaluated. The theoretical results are illustrated to be effective by several numerical examples.