Cluster synchronization for fractional-order neural networks with nonlinear coupling

Abstract

This study investigates the cluster synchronization control of fractional-order neural networks with uncertain parameters and nonlinear coupling. Initially, projection techniques are utilized to decompose the nonlinear coupling function into oscillatory and linear parts. Inequality techniques are then employed to handle these parts separately, effectively mitigating the adverse impact of nonlinear coupling on the network. To conserve resources, a pinning impulsive control strategy based on the average impulsive interval is selected. A universal Lyapunov function for the entire network is constructed, providing sufficient conditions for the fractional-order neural networks to achieve cluster synchronization. Moreover, the applicability of these findings to integer-order neural networks with nonlinear coupling is also demonstrated. The validity of the theoretical results is further confirmed through numerical simulations.