General model and physical principles of memristor neurons

Locally active memristors (LAMs), owing to their excellent intrinsic brain-like properties, have become fundamental building blocks for constructing spiking neurons and implementing brain-inspired computing. Although a variety of LAM-based neurons and their computational networks have been reported, the diversity of internal physical mechanisms and neuronal structural principles makes it challenging to establish a unified theoretical framework for memristive neurons starting from microscopic physical mechanisms. This difficulty hinders the unified analysis and quantitative characterization of neural behaviors across different material systems, and restricts the widespread application of LAMs in the field of neuromorphic computing. To address this issue, this work circumvents the intricate microscopic material details and physical processes inside LAMs, and instead starts from their macroscopic electrical port characteristics and mathematical models to extract the inherent neuron-like behavioral features of the devices themselves. On this basis, we construct a general memristive neuron model applicable to different material systems and physical mechanisms, and provide the physical structural principles and parameter calculation principles underlying the model construction. This generic neuron model features a minimal topology and is capable of realizing all eight possible combinations of second-order and third-order memristive neuron designs, thereby overcoming the long-standing trial-and-error approach to determining circuit topology and parameters. Furthermore, taking a modified Chua Corsage Memristor as an illustrative example, the theoretical design and calculations of second- and third-order memristive neuron circuits are validated. Typical brain-like behaviors, including resting states, periodic spiking, burst spike firing and chaotic spiking, are reproduced, and the formation mechanisms of different firing patterns are elucidated. This paper provides a rigorous theoretical methodology for the design and analysis of memristive spiking neurons in future brain-inspired computing, as well as for other memristive circuits such as chaotic circuits.