Pinning impulsive cluster synchronization of uncertain complex dynamical networks with multiple time-varying delays and impulsive effects

Abstract

The pinning impulsive cluster synchronization problem of uncertain complex community networks with impulsive effects, internal delay and coupling delay is studied in this paper. Particularly, the local dynamics of nodes in different communities are assumed to be nonidentical and two kinds of delays are all time-varying. A novel impulsive comparison principle with multiple time-varying delays is established to conquer the difficulties caused by various delays and impulsive effects. Based on the Lyapunov stability theory and pinning impulsive control techniques, some sufficient conditions depending on impulsive intervals and delays are derived to guarantee cluster synchronization of the community networks by pinning a small fractional of network nodes. The upper bound of the internal delay and coupling delay can be estimated by the obtained conditions. The theoretical results in this paper can be seen as extensions of the previous related works. Finally, a numerical simulation is presented to illustrate the validity of our results.