Hybrid amplitude dynamics analysis of a new locally active memristive neural network with application to medical image encryption

Abstract Memristive neural networks are widely studied for rich dynamics, but amplitude dynamics and flexible oscillation control are still not well understood. First, a new locally active memristor is introduced, showing multistability and nonvolatility, and these properties are verified. Then, the memristor is embedded as an autapse in a Hopfield neural network to form a new memristive Hopfield neural network (MHNN). The MHNN dynamics are analyzed, and chaos is confirmed using Lyapunov exponents and phase portraits. Next, hybrid amplitude dynamics are demonstrated: by tuning memristor parameters, stimulus current, and initial states, the MHNN switches between periodic and chaotic oscillations and adjusts amplitudes over a wide range. Finally, an FPGA implementation is presented, and a medical image encryption scheme based on chaotic synchronization is designed, avoiding key transmission through the channel. Simulations show strong security performance, supporting the MHNN for secure medical image transmission.