Impulsive Synchronization of Derivative Coupled Neural Networks With Cluster-Tree Topology

Abstract

This article is devoted to discussing the exponential synchronization for a kind of delay derivative coupled neural networks with stochastic disturbance and multiple time-varying delays. To simulate more practical situations and widen the synchronization application fields in network science, the coupled neural networks with cluster-tree topology structure is studied by applying a novel impulsive pinning control strategy, which skillfully considered the neural networks in current cluster that directly linked to the neural networks in other clusters. Since the existence of delayed impulses, the general comparison principle for normal impulsive differential equations is efficiently extended. In view of the concept of average impulsive interval, the parameters classification discussion method and the mathematical induction method, some judgement conditions for achievement of the cluster synchronization on derivative coupled neural networks are derived. Additionally, the exponential convergence velocity of the derivative coupled neural networks is accurately estimated. Finally, numerical examples are presented to demonstrate the effectiveness of the control strategy and the theoretical results.