Cluster Synchronization for Stochastic Coupled Neural Networks with Nonidentical Nodes via Adaptive Pinning Control

The cluster synchronization was investigated by adaptive pinning control for coupled neural networks (CNNs) with stochastic disturbances. In CNNs, nodes can only synchronize with the corresponding isolated nodes in the same cluster, and the synchronization status of nodes is different in different clusters. Then, adaptive pinning controllers are set on each cluster to realize cluster synchronization, which can select appropriate pinning nodes and eliminate the unknown feedback gain. In addition, for nonlinear functions in CNNs, an NCF (acceptable nonlinear coupling function class) method is used to approximate nonlinear functions to linear functions. On account of the adaptive pinning control strategy, the sufficient condition of mean-square exponential stability for CNNs is given by using M-matrix technique. Finally, the effectiveness of cluster synchronization under the adaptive pinning control are verified by two simulations.