Mott Memristors and Neuronal Ion Channels: A Qualitative Analysis

Memristive devices have earned increased recognition over the past decade, owing to their application in memory and neuromorphic systems. Recently, memristive devices have found a propitious role in Spiking Neural Networks. This is partly attributed to an emerging family of memristive devices that are volatile. Volatile memristors, especially Mott memristors, have been used to implement Leaky Integrate and Fire neurons along with neuron circuits with richer dynamics, referred to as neuristors. The Mott memristor is often compared to voltage-gated ion channels in the Hodgkin-Huxley neuron model. However, voltage-gated ion channels in the Hodgkin-Huxley model do not exhibit voltage hysteresis in their quasi-static I-V characteristics, a critical property of Mott memristors. We discuss the association between Mott memristors based on joule heating and the Hodgkin-Huxley voltage-gated ion channels, and we prove that they are qualitatively dissimilar. Consequently, we propose a hypothetical potassium current-gated ion channel that exhibits voltage hysteresis. We simulate a Mott memristor Pearson-Anson oscillator and a current-gated ion channel oscillator. We use the nullcline plots and bifurcation diagrams of the circuits to demonstrate that both circuits are qualitatively similar. We further show that both circuits produce oscillations through a supercritical Andronov-Hopf bifurcation and have a similar oscillation-generation mechanism. We conclude that for the Mott memristor to share qualitative similarity to a neuronal ion channel, the channel must be current-gated rather than voltage-gated. Our aim is to supplement the understanding of how hardware neurons relate to their biological counterparts, which is a crucial first step towards implementing better brain-inspired systems.