In this paper, we build a general model of memristors suitable for the simulation of event-based systems, such as hardware spiking neural networks, and more generally, neuromorphic computing systems. We extend an existing general model of memristors - the Generalised Metastable Switch Model - to an event-driven setting, eliminating errors associated discrete time approximation, as well as offering potential improvements in terms of computational efficiency for simulation. We introduce the notion of a volatility state variable, to allow for the modelling of memory-dependent and dynamic switching behaviour, succinctly capturing and unifying a variety of volatile phenomena present in memristive devices, including state relaxation, structural disruption, Joule heating, and drift acceleration phenomena. We supply a drift dataset for titanium dioxide memristors and introduce a linear conductance model to simulate the drift characteristics, motivated by a proposed physical model of filament growth. We then demonstrate an approach for fitting the parameters of the event-based model to the drift model.
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