A new third-order memristive neuron and its complex neuromorphic dynamics near the edge of chaos

Due to the practical constraints imposed by Moore's Law and the von Neumann computing architecture, neuromorphic computing has come forward as a more favorable alternative for information processing. Current hardware approaches to neuromorphic computing rely on complex transistor circuits to simulate the biological functions of neurons and synapses. However, these can be more faithfully simulated by memristors that naturally express neuromorphic nonlinear dynamics. Producing neuromorphic action potentials theoretically requires a minimum of a third-order neuron circuit. To explore the neuromorphic properties of memristors, this paper proposes a novel locally active memristor (LAM), based on which we designed a second-order neuron and a third-order neuron circuit. Based on local activity theory, we illustrate that the two neuron circuits built on LAM and located at the edge of chaos (EoC) can produce eighteen different kinds of neuromorphic action potential phenomena in the vicinity of the EoC using Hopf bifurcation. Furthermore, we also provide a theoretical analysis of the generating mechanism of neuronal action potentials through the zero-pole trajectories of neuronal admittance functions and demonstrate that the neuromorphic behaviors emerge either on, or near the EoC domain.