Abstract
A model of neuronal behaviour capable of accounting for the oscillatory, plateau and rebound properties of biological neurons is derived, discussed and analysed. The model is based on a piecewise linear form of the FitzHugh-Nagumo equations, but reduces to a set of maps very similar to those of the Hopfield model (1982). In particular, the binary description of individual neurons and the well studied form of the synaptic current Sigma JijSj are preserved, although the model is capable of reproducing behaviours on the slow timescales characteristic of plateau and oscillation. By coupling two model cells together a mutually inhibitory or half-centred oscillator and an oscillator, fixed-phase follower pairs are constructed.
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