Fixed-Time Synchronization of Fractional-Order Hopfield Neural Networks with Proportional Delays

Abstract

This article explores the fixed-time synchronization of fractional-order Hopfield neural networks incorporating proportional delays. Unlike finite-time synchronization, where the convergence time varies based on the initial synchronization errors, fixed-time synchronization allows for a predetermined settling time that remains independent of initial conditions. To achieve fixed-time synchronization, two types of feedback control strategies incorporating fractional integrals are employed: one based on state feedback and another utilizing a controller designed with a Lyapunov function and an exponential function. By designing appropriate Lyapunov functions and employing inequality techniques, multiple sufficient conditions were established to guarantee the fixed-time synchronization of the considered systems under these control strategies. Finally, two numerical examples are presented to demonstrate the validity and practical relevance of the theoretical findings.