Fixed/Preassigned Time Synchronization of Impulsive Fractional-Order Reaction–Diffusion Bidirectional Associative Memory (BAM) Neural Networks

Abstract

This study delves into the synchronization issues of the impulsive fractional-order, mainly the Caputo derivative of the order between 0 and 1, bidirectional associative memory (BAM) neural networks incorporating the diffusion term at a fixed time (FXT) and a predefined time (PDT). Initially, this study presents certain characteristics of fractional-order calculus and several lemmas pertaining to the stability of general impulsive nonlinear systems, specifically focusing on FXT and PDT stability. Subsequently, we utilize a novel controller and Lyapunov functions to establish new sufficient criteria for achieving FXT and PDT synchronizations. Finally, a numerical simulation is presented to ascertain the theoretical dependency.

Keywords

• fractional-order
• impulse effect
• fixed-time synchronization
• predefined-time synchronization