Effect of large delay on pinning impulsive synchronization control: A strict comparison principle

Abstract

SummaryOver the past decades, various successful results have shown the discoveries and progress of impulsive synchronization. Yet, little attention has been devoted to the effects of the impulsive elasticity coefficient on network synchronization for both impulsive control problems and impulsive disturbance problems. In this work, we study impulsive pinning synchronization for coupled neural networks from a large delay perspective. Some flexible synchronization criteria are derived based on the average impulsive interval method. It has shown that synchronization of coupled neural networks with arbitrarily finite delay can be achieved via controlling a small fraction of nodes. Specifically, by applying a strict comparison principle for impulsive delayed neural networks, the effects of the impulsive elasticity coefficient on synchronization are revealed to be dissimilar from the case of delay‐free neural networks. One can verify that increasing the elasticity coefficient may bring a desynchronizing impact on the original synchronized networks. More ulteriorly, the generated criteria will still hold if the delay is sufficiently large, which implies that the delay is independent of the size of the impulsive interval. Our work is an essential step toward investigating the role of the elasticity coefficient on synchronization. Furthermore, the synchronization region of different impulsive weights, impulsive intervals, and impulsive control proportions are described thoroughly.