Hopfield Neural Network Dynamics with Dual Memristor Unidirectional Synaptic Connections and Its Application

The study of the dynamic properties of neural networks has always been a major area of interest, and an important way for the central nervous system to process information is by inducing changes in synaptic strength between neurons. However, the dynamic analysis of the unidirectional synaptic connection weights of more than two memristors is still insufficient. This paper proposes a Two-Sinusoidal Memristor Hopfield Neural Network (TSM-HNN), in which two identical sinusoidal memristors are used to replace the synaptic weights in the Hopfield neural network. The stability of the model is distributed on the initial state plane of the two memristors, featuring a planar equilibrium set. The numerical simulation method is used to study the complex dynamic behaviors of TSM-HNN, including the state transitions with varying coupling gains, the coexistence of attractors under different initial states with the same parameters, and the coexisting behaviors of memristive initial offsets and state variable offsets where identical topological patterns exist at different positions. Meanwhile, a hardware circuit centered at the STM32 microcontroller is designed to verify the correctness of the numerical simulations and the feasibility of the TSM-HNN. Finally, the TSM-HNN is applied to image encryption, and a series of analyses on its security are conducted to confirm the security performance of the model in image transmission.