Synchronization of fractional-order delayed neural networks with reaction–diffusion terms: Distributed delayed impulsive control

Abstract

In this study, a new fractional Halanay-like impulsive differential inequality, which considers the system delay and impulse delay, is proposed for the first time. And accordingly, the quasi-synchronization problem of delayed fractional-order coupled reaction–diffusion neural networks (CRDNNs) is investigated. It is important to know that there are still relatively few studies on the impulsive synchronization control of fractional-order systems with time delay, and this study is an effective complement to this relevant field. To achieve quasi-synchronization, the distributed delayed impulsive control strategy is applied, which utilizes the local state information and the weighted average delayed information of other available neurons. Then, based on Wirtinger inequality, Lyapunov stability theory, and the properties of Mittag-Leffler function, some quasi-synchronization criteria are derived by solving some linear matrix inequalities (LMIs). Finally, a numerical simulation is provided to demonstrate the effectiveness of theoretical results, and reveal the effects of impulse delay and fractional order on the system synchronization rate.