My first "math" paper has now been published in the prominent journal Chaos, Solitons & Fractals and can be found here. In this paper we formally define and generalise a class of Simple Volatile Memristors (SVMs), which notably includes various recently reporten fluidic iontronic memristors. With some relatively straightforward mathematical analysis we can make some remarkably general statements on the behaviour of any SVM, such as linking the device spatial symmetry to which type (type 1 or 2) of memristor the SVM is and providing a link between the SVM timescale and its hysteresis loop.
Furthermore we reduce a somewhat convoluted system of equations that describes a physical SVM based neuromorphic spiking circuit to a simple two-dimensional dynamical system featuring only a handful of parameters. This model has the fascinating property of being fully physically plausible, being directly derived from physical equations, while also being mathematically tractable as two-dimensional system. Using this model we show how the natural presence of voltage noise can induce novel forms of stochastic spiking.
