A simple mathematical theory for Simple Volatile Memristors and their spiking circuits

• Main Authors: Kamsma, T. M, van Roij, R, Spitoni, C
• Format: Journal Article
• Language: English
• Published: 19-09-2024
• Subjects: Physics - Soft Condensed Matter; Quantitative Biology - Neurons and Cognition
• DOI: 10.48550/arxiv.2404.08647

Chaos, Solitons & Fractals (2024), Vol. 186, 115320 In pursuit of neuromorphic (brain-inspired) devices, memristors
(memory-resistors) have emerged as effective components for emulating neuronal
circuitry. Here we formally define a class of Simple Volatile Memristors (SVMs)
based on a simple conductance equation of motion from which we build a simple
mathematical theory on the dynamics of isolated SVMs and SVM-based spiking
circuits. Notably, SVMs include various fluidic iontronic devices that have
recently garnered significant interest due to their unique quality of operating
within the same medium as the brain. Specifically we show that symmetric SVMs
produce non self-crossing current-voltage hysteresis loops, while asymmetric
SVMs produce self-crossing loops. Additionally, we derive a general expression
for the enclosed area in a loop, providing a relation between the voltage
frequency and the SVM memory timescale. These general results are shown to
materialise in physical finite-element calculations of microfluidic memristors.
An SVM-based circuit has been proposed that exhibits all-or-none and tonic
neuronal spiking. We generalise and analyse this spiking circuit,
characterising it as a two-dimensional dynamical system. Moreover, we
demonstrate that stochastic effects can induce novel neuronal firing modes
absent in the deterministic case. Through our analysis, the circuit dynamics
are well understood, while retaining its explicit link with the physically
plausible underlying system.