Global Asymptotic Stability and Adaptive Ultimate Mittag–Leffler Synchronization for a Fractional-Order Complex-Valued Memristive Neural Networks With Delays

Abstract

This paper investigates some dynamic behaviors for a fractional-order complex-valued memristive neural networks (FCVMNNs) with delays. A new mathematical expression of the complex-value memductance (memristance) is proposed according to the feature of the complex-valued memristor-based neural networks and a new class of FCVMNNs with delays is designed. Based on the framework of Filippov solution and differential inclusion theory, the sufficient conditions are given first to guarantee the global uniform asymptotic stability for the new FCVMNNs with delays, by using fractional-order Leibniz rule and a Razumikhin-type method. In addition, a complex-value adaptive controller is designed to achieve ultimate Mittag–Leffler synchronization between two FCVMNNs with delays. Numerical simulations are given to show the effectiveness of the theoretical results.