A simple mathematical theory for Simple Volatile Memristors and their spiking circuits
arxiv(2024)
摘要
In pursuit of neuromorphic (brain-inspired) devices, memristors
(memory-resistors) have emerged as promising candidates for emulating neuronal
circuitry. Here we mathematically define a class of Simple Volatile Memristors
(SVMs), which notably includes various fluidic iontronic devices that have
recently garnered significant interest due to their unique quality of operating
within the same medium as the brain. We show that symmetric SVMs produce non
self-crossing current-voltage hysteresis loops, while simple 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. Additionally, 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.
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