A novel memristive neuron and its neuromorphic dynamics on edge of chaos

The exponential growth in demand for computing capacity drives transistor scaling to slow down and von Neumann architecture to encounter energy efficiency bottlenecks. A promising solution is memristor-based brain-like computing in which each memristor functionally replaces elaborate digital circuits, leading to adaptive computing. Locally active memristors naturally embody the capability to amplify infinitesimal fluctuations in energy and so can be used to imitate biological neurons to generate neuromorphic behaviors. This paper presents the instability problem of local active memristors and the design principle of memristor neuron circuits for the first time, and proposes an improved Chua corsage memristor (ICCM, a locally active memristor) for designing memristor-based neurons. Based on the ICCM and the design principle of memristor-based neurons, we design second-order and third-order neurons, and analyze their neuromorphic dynamics both theoretically and by numerical simulations. Using Chua’s theory of local activity, we demonstrate that under the stimulation of neuron input voltages, the two ICCM-based neuron circuits can generate rich neuromorphic behaviors near the edge of chaos via Hopf bifurcations, such as periodic spikes (action potentials), burst spike, burst-number adaptation, self-sustaining oscillations, chaotic oscillation and so on.