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

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.

Automated summary

This article investigates the predefined-time synchronization of fractional-order memristive competitive neural networks with time-varying delays. Two distinct discontinuous bilayer predefined-time control schemes based on fractional integrals are proposed to address the two-layer structural characteristics of CNNs. By utilizing predefined-time stability theorems and applying fractional-order differential inequalities and other inequality techniques, concise criteria are obtained to ensure the predefined-time stability of two FMCNNs in terms of algebraic inequalities. The predefined time parameter is arbitrary and does not depend on the initial values. Two examples are provided to validate the theoretical results.