Locally Active Memristor Cooperatively-Controlled Fast-Slow Dynamics in Morris–Lecar Neuron Model and FPGA Implementation

Translating the complex dynamics of biological nervous systems into engineered models is crucial for understanding the essence of intelligence and creating human-like artificial intelligence. This article presents a four-dimensional memristive Morris-Lecar model, constructed by coupling a locally active memristor (LAM) with the Morris-Lecar model, which features fast-slow dynamics. Through stability analysis of equilibrium points, the potential mechanism is qualitatively investigated by which three types of equilibrium points trigger neuronal oscillatory activity. Different dimensions of bifurcation diagrams and other numerical techniques reveal that neuronal firing activity and its dynamic characteristics are regulated by three factors: 1) LAM; 2) the slow variable; and 3) ion channels. Based on bursting activity, the fast-slow variable analysis method is employed to study fold and Hopf bifurcations, and the fast-slow dynamics under synergistic control are elucidated. Notably, coexisting attractors are discovered and found to be closely related to LAM. Finally, the neuronal model is implemented on an FPGA to generate firing activities with diverse dynamic characteristics.