Unified synchronization criteria in an array of coupled neural networks with hybrid impulses.

Abstract

This paper investigates the problem of globally exponential synchronization of coupled neural networks with hybrid impulses. Two new concepts on average impulsive interval and average impulsive gain are proposed to deal with the difficulties coming from hybrid impulses. By employing the Lyapunov method combined with some mathematical analysis, some efficient unified criteria are obtained to guarantee the globally exponential synchronization of impulsive networks. Our method and criteria are proved to be effective for impulsively coupled neural networks simultaneously with synchronizing impulses and desynchronizing impulses, and we do not need to discuss these two kinds of impulses separately. Moreover, by using our average impulsive interval method, we can obtain an interesting and valuable result for the case of average impulsive interval T_a=∞. For some sparse impulsive sequences with T_a=∞, the impulses can happen for infinite number of times, but they do not have essential influence on the synchronization property of networks. Finally, numerical examples including scale-free networks are exploited to illustrate our theoretical results.