Memristor neurons with symmetric activity on the edge of chaos: Mono-/biphasic complex neuromorphic behaviors

The biphasic action potential represents a crucial neuromorphic behavior of biological neurons. However, most existing memristor-based neurons currently simulate only monophasic action potentials, and the mechanisms underlying biphasic action potential generation remain incompletely understood. To address this gap, this study proposes a novel locally active memristor (LAM) model featuring a symmetric locally active domain (LAD). Theoretical and simulation analyses are conducted to investigate its local activity, edge of chaos (EoC), and small-signal equivalent circuit. Subsequently, using locally active and EoC theories, we theoretically investigated the biphasic neuromorphic dynamics and their underlying mechanism in second-order/third-order memristor-based neuronal circuits. The results demonstrate that neurons operating near the EoC via supercritical/subcritical Hopf bifurcations can generate not only biphasic action potentials but also a wide range of monophasic spike patterns and other neuromorphic behaviors, including periodic spiking, bursting, accommodation, self-sustaining oscillations, and chaotic dynamics of aberrant neuronal firing. Furthermore, EoC theory clarifies the physical origins of these bimodal dynamics: under bidirectional input pulse perturbations, neurons exhibit both bimodal and monomodal behaviors through Hopf bifurcations occurring near the odd-symmetric EoC.