Predefined-time synchronization of fractional-order memristive competitive neural networks with time-varying delays

Abstract

This article focuses on the predefined-time synchronization (PTS) of fractional-order memristive competitive neural networks (FMCNNs) with time-varying delays. According to the two-layer structural characteristics of CNNs, two kinds of distinctive discontinuous bilayer predefined-time control schemes with the fractional integrals are proposed: one is the double controllers based on piecewise Lyapunov function and the other is a controller with Lyapunov function and exponential function. Using the predefined-time stability theorems and applying fractional-order differential inequalities and other inequality techniques, some effective criteria are obtained to assure the PTS of two FMCNNs in terms of algebraic inequalities, which are very succinct and avert complicated calculations. Besides, the predefined time (PT) is set to an arbitrary positive parameter in these controllers and is entirely irrelevant to the initial values. Finally, two concrete examples are given to verify the theoretical results.