Fixed-time synchronization of time-varying delayed BAM neural networks in quaternion variable

Abstract This article explores the Fixed-time (FXT) synchronization of time-varying delayed BAM neural networks in quaternion variable. By leveraging fixed-time stability theory, the Lyapunov functional method, and specific inequality techniques, a novel synchronization criterion is proposed to ensure convergence within a predefined fixed time, independent of initial conditions. Additionally, a more precise calculation of the settling time is provided, highlighting its independence from the system’s initial states. To facilitate the synchronization process, a nonlinear delayed controller is introduced. The theoretical findings are substantiated through a numerical example, confirming the framework’s effectiveness.