Second-order locally active memristor based neuronal circuit

Brain-like neurons inspired by biology are critical in constructing neuromorphic computing architectures with high energy efficiency. Memristors, characterized by their nanoscale and nonlinearity, have emerged as prime candidates for realizing artificial neuron. Considering the integration density, we propose a voltage-controlled locally active memristor (LAM) with second-order complexity. In contrast to first-order memristors, the locally active domains (LADs) of the second-order memristor cannot be determined solely by the DC V–I curve, then the small-signal method is introduced to identify all LADs, which are classified as Class I and Class II. Based on the capacitive or inductive characteristics of the memristor operating at different locally active voltages judged by its frequency response, a simple third-order neuronal circuit that incorporates compensate components such as an inductor or a capacitor can be built. Further exploration on the edge of chaos relying on the admittance function measures the type and value of the compensate component. We take the operating points with capacitive features as an example, which require an inductive device in series with the memristor and a biasing voltage source. The built neuronal circuit replicates twelve brain-like behaviors, especially class I and class II excitability, all-or-nothing firing, and refractory period, whose generation mechanism is investigated via the dynamic map, Lyapunov exponents, and bifurcation plot. The circuit simulation results also demonstrate the effectiveness of theoretical analyses on the second-order memristor and the third-order memristive neuron.