Dynamic analysis and implementation of a multi-stable Hopfield neural network

Abstract

To further investigate the influence of multistability on dynamic memory and information processing in biological neurons, this paper constructs a Hopfield neural network (HNN) model with memristive synaptic weights. The dynamical behaviors are systematically analyzed via bifurcation diagrams, Lyapunov exponent spectra, and phase portraits. The results demonstrate that the HNN not only exhibits bistability through variations in non-memristive initial values but also reveals multistability under altered memristive initial conditions, accompanied by observable transient chaotic phenomena. Furthermore, under appropriate initial conditions, the system generates infinite pairs of coexisting chaotic and periodic attractors with structural similarity and spatial offset, manifesting a symmetric multistability. Experimental validation using FPGA-based hardware implementation confirms the consistency between theoretical analysis and numerical simulations. Additionally, the application of generated chaotic sequences to image encryption is explored through numerical simulations and statistical analyses, demonstrating satisfactory encryption performance.