Discrete neuron model based on locally active memristor: Dynamics analysis and circuit implementation

The integration of locally active memristors (LAMs) into low-dimensional discrete neuron models presents a novel and prospective approach to understanding complex neuronal dynamics. In this study, we propose a novel discrete memristor-driven neuron (DMDN) model constructed using a discrete LAM (DLAM) that operates at the edge of chaos. We integrate a trigonometric-function-driven DLAM into a two-dimensional (2D) map-based neuron framework, replacing the traditional linear ionic recovery variable with a nonlinear coupling mechanism. This modification generates a wide range of neuronal dynamics influenced by memristive parameters, including periodic, quasi-periodic, chaotic, and hyperchaotic firing behaviors. Furthermore, the DMDN model shows sensitivity to initial conditions and supports the coexistence of multiple attractors. These dynamical characteristics are illustrated via bifurcation diagrams, Lyapunov exponents, phase portraits, time series, and attractor basins. To validate the feasibility of DMDN model, both the implementation of PSIM-based analog simulation and FPGA-based digital hardware are elaborated. The primary contribution of this work is the development of a new discrete neuron model that enhances neuronal dynamics and provides a promising pathway toward an efficient neuromorphic computing architecture.