Summary: J. Phys.A: Math. Gen. 23 (1990) 3835-3859. Printed in the UK
A network of oscillators'
i F Abbott
Physics Department, Brandeis University, Waltham, MA 02254, USA
Received 11 December 1989
Abstract. A model of neuronal behaviour capable of accounting for the oscill&
tory, 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 t.o a set of maps very similar to those of the Hopfield model.
In particular, the binary descript.ion of individual neurons and the well studied form
of the synaptic current J;, S, are preserved, although the model is capable of re-
producing 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. The behaviour of a net-
work of oscillatory cells is analysed with particular attention to phase-locking. The
response of a single cell to a square wave input provides a mean-field approximation
for large networks. This approach is compared with the results of a phase-coupling
description of the oscillators. The network of oscillators discussed can be used to con-
struct associative memories in which the signal for memory recall is not fixed-point
behaviour but phase locking. The performance and capacity of such phase-locking