Cluster synchronization of delayed coupled neural networks: Delay-dependent distributed impulsive control.

Abstract This paper investigates the issue of cluster synchronization (CS) for the coupled neural networks (CNNs) with time-varying delays via the delay-dependent distributed impulsive control. A new Halany-like inequality, where delayed impulses are taken into consideration, is proposed. Based on the Lyapunov theory and the new differential inequality, sufficient conditions of CS for delayed CNNs with fixed and switching coupling topology are obtained, respectively. Moreover, delay-dependent distributed impulsive controllers with fixed or switching topology are designed thereby. Finally, we present a numerical example of CNNs with fixed or switching coupling to verify the effectiveness of our results, respectively.