Fixed-time Synchronization of Coupled Memristive Complex-valued Neural Networks

Abstract

By directly proposing discontinuous complex-valued controllers and constructing Lyapunov functions for complex-valued networks, this article is devoted to fixed-time (F-T) synchronization of coupled memristive complex-valued neural networks (MCNNs) with time-varying delays. Above all, a new theorem for F-T stability is established to reduce the conservatism of the existing work in terms of conditions and the estimate of stability time. Subsequently, under the framework of the complex-valued sign function, several simplified complex-valued F-T control laws are proposed by excluding the linear part in previous F-T design. Furthermore, without splitting the addressed coupled MCNNs into real-valued submodels in the theoretical analysis, several sets of conditions of F-T synchronization are obtained for coupled MCNNs by means of the theory of complex-variable functions and the improved F-T stability. Lastly, the developed control strategies and the results on F-T synchronization are verified by the presence of a numerical example.