Affiliation:
1. School of Mathematical Sciences Qufu Normal University Shandong China
2. School of Network Security and Information Technology Yili Normal University Yining China
Abstract
SummaryThe cluster synchronization problem of stochastic two‐layer networks with infinite distributed delays is concerned. Firstly, we study the cluster synchronization of the first layer (leader‐layer) network with the average state of each cluster of sets as synchronization target. Secondly, we design a delayed pinning impulsive controller to synchronize the second layer (follower‐layer) network to the first layer network in a mean square cluster sense. Based on stochastic impulsive analysis and Lyapunov stability theory, some sufficient conditions for cluster synchronization are obtained. Finally, the effectiveness of the theoretical results is verified through numerical simulations.
Funder
Natural Science Foundation of Shandong Province
China Postdoctoral Science Foundation
National Natural Science Foundation of China