Event-triggered synchronization of fractional-order complex-valued BAM neural networks with application to image encryption

This study explores the issue of synchronizing fractional-order complex-valued bidirectional associative memory neural networks with time-varying delays, employing an event-triggered control (ETC) strategy. Unlike existing approaches that rely on decomposition methods, this study employs a Lyapunov direct approach to derive sufficient conditions for synchronization. The proposed ETC mechanism significantly reduces communication and energy consumption by updating control signals only at event-triggered instants determined by a rigorously defined triggering condition. Using fractional Lyapunov-Krasovskii functionals and Razumikhin-type stability criteria, the paper guarantees global Mittag-Leffler synchronization despite the presence of fractional-order dynamics and time delays. Furthermore, the proposed ETC scheme ensures practical implementation by excluding Zeno behavior through strictly positive inter-event intervals. The effectiveness of the theoretical results is demonstrated through numerical simulations, and their practical relevance is highlighted by applying the proposed synchronization strategy to secure image encryption.