  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.
