A Multistable Discrete Memristor and Its Application to Discrete-Time FitzHugh–Nagumo Model

Abstract

This paper presents a multistable discrete memristor that is based on the discretization of a continuous-time model. It has been observed that the discrete memristor model is capable of preserving the characteristics of the continuous memristor model. Furthermore, a three-dimensional memristor discrete-time FitzHugh–Nagumo model is constructed by integrating the discrete memristor into a two-dimensional FitzHugh–Nagumo (FN) neuron model. Subsequently, the dynamic behavior of the proposed neuron model is analyzed through Lyapunov exponents, phase portraits, and bifurcation diagrams. The results show multiple kinds of coexisting hidden attractor behaviors generated by this neuron model. The proposed approach is expected to have significant implications for the design of advanced neural networks and other computational systems, with potential applications in various fields, including robotics, control, and optimization.