Synchronization in an array of coupled neural networks with delayed impulses: Average impulsive delay method

In the paper, synchronization of coupled neural networks with delayed impulses is investigated. In order to overcome the difficulty that time delays can be flexible and even larger than impulsive interval, we propose a new method of average impulsive delay (AID). By the methods of average impulsive interval (AII) and AID, some sufficient synchronization criteria for coupled neural networks with delayed impulses are obtained. We prove that the time delay in impulses can play double roles, namely, it may desynchronize a synchronous network or synchronize a nonsynchronized network. Moreover, a unified relationship is established among AII, AID and rate coefficients of the impulsive dynamical network such that the network is globally exponentially synchronized (GES). Further, we discuss the case that time delays in impulses may be unbounded, which has not been considered in existing results. Finally, two examples are presented to demonstrate the validity of the derived results.