Impulsive Synchronization of Derivative CNNs with Cluster-Tree Topology

In this chapter, we discusses the global exponential synchronization for a class of delay derivative coupled neural networks with multiple time-varying delays and stochastic disturbance. To broaden the fields of synchronization applications in network science, consider cluster-tree topology structure of the coupled neural networks, a novel impulsive pinning control strategy is proposed, which skillfully considered the neural networks in current cluster that directly linked to the neural networks in other clusters. Due to the existence of delayed impulses, the extended comparison principle is efficiently used for general impulsive differential equations. In view of the concept of average impulsive interval, some sufficient conditions and exponential convergence velocity for the cluster synchronization on derivative coupled neural networks are derived by applying the mathematical induction method and the parameters classification discussion method. Finally, the effectiveness of the control strategy and the theoretical results is illustrated by the numerical examples.