Pinning synchronization criterion for impulsive dynamical networks

This paper focuses on the problem of global synchronization for impulsive coupled dynamical networks via pinning control. Controlling impulsive synchronization of the network by changing the differences between some chosen nodes and the reference signal step by step is the main idea discussed in this paper, regardless of whether there is a synchronized or desynchronized impulses for the dynamical networks. In the previous literature, results are devoted to investigating criterion for synchronization with impulsive control on all the nodes in dynamical networks. Thus some questions arises: What is the relation between strength of impulsive signal and the impulsive interval? How do the chosen pinning nodes affect the dynamics of the network? In this paper, a synchronization criterion is derived for impulsive dynamical networks for pinning control, and clear relations between the strength of impulsive signal, the impulsive interval, and pinning nodes are provided. Numerical examples are given at last to show the effectiveness of results.