Cluster synchronization of stochastic two-layer delayed neural networks via pinning impulsive control

This paper considers the cluster synchronization of stochastic two-layer delayed neural networks via pinning impulsive control. First, the cluster synchronization of the first layer (leader-layer) network is explored by taking the average state of each subnet as the synchronization target. Then, a pinning impulsive controller is designed to synchronize the second layer (follower-layer) network to the leader-layer network in the mean square cluster sense. Based on the stochastic impulsive analysis and Lyapunov stability theory, some sufficient conditions for cluster synchronization are strictly obtained. At last, the correctness of the theoretical result is illustrated by a numerical example. Compared with previous works, the proposed network model is closer to the real networks and the control strategy is more energy efficient.