Fixed-Time Synchronization of Memristive Inertial BAM Neural Networks via Aperiodic Switching Control

This paper investigates the fixed-time stabilization and synchronization of a class of memristor inertial BAM neural networks with mixed delays using a non-order reduction method. By constructing a Lyapunov function and leveraging novel fixed-time stability lemmas, we design an aperiodic switching controller that addresses the inflexibility of traditional periodic control in high-order systems. Theoretical analysis proves that the controller ensures system states converge to equilibrium within a fixed time, independent of initial conditions. The inclusion of mixed delays further enhances the model’s practicality. Notably, the proposed method is applied to secure communication, demonstrating its capability to protect information transmission in realworld scenarios. Numerical simulations validate the effectiveness of the approach, with secure communication experiments specifically confirming its encryption potential. This work bridges theoretical control design with critical cybersecurity applications.