Cluster Synchronization in Delayed Networks With Adaptive Coupling Strength via Pinning Control

Abstract

Many previous studies have indicated that pinning control and adaptive feedback control are two of most effective strategies for achieving synchronization. In this paper, we present a mixed method integrating the two control strategies to realize cluster synchronization in delayed networks with directed couplings. Based on Lyapunov stability theory and matrix theory, several criteria on cluster synchronization are obtained. Compared with the previous results on cluster synchronization, the obtained criteria can be applied to delayed network with non-identical nodes, directed couplings, and time-varying coupling strength. Finally, numerical simulations are performed to verify the theoretical results.