A simple mathematical theory for Simple Volatile Memristors and their spiking circuits
arXiv:2404.08647 · doi:10.1016/j.chaos.2024.115320
Abstract
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.
References in corpus (13)
- Memory effects in complex materials and nanoscale systems
- Brain-inspired computing: We need a master plan
- Long-term memory and synapse-like dynamics in two-dimensional nanofluidic channels
- Modeling of emergent memory and voltage spiking in ionic transport through angström-scale slits
- Brain-inspired computing with fluidic iontronic nanochannels
- Iontronic Neuromorphic Signaling with Conical Microfluidic Memristors
- Dramatic pressure-sensitive ion conduction in conical nanopores
- Beyond the Tradeoff: Dynamic Selectivity in Ionic Transport and Current Selectivity
- Pressure-sensitive ion conduction in a conical channel: optimal pressure and geometry
- Confinement-controlled rectification in a geometric nanofluidic diode
- Unveiling the capabilities of bipolar conical channels in neuromorphic iontronics
- Advanced iontronic spiking modes with multiscale diffusive dynamics in a fluidic circuit
- Analytic theory of nonlinearly coupled electrokinetics in nanochannels