Some properties of randomly connected networks of neuron-like elements with refractory

Abstract

Dynamic properties of randomly connected networks consisting of neuron-like elements with refractory are investigated from a macroscopic point of view. Equations describing the transition of the activity level of the network — a macroscopic state — are derived under some hypotheses on the stochastic properties of the network. The equations are characterized by a set of parameters which are determined by distributions of the threshold values of elements and the weighting values of connection between elements. It is shown that a network behaves like a monostable, bistable or astable circuit when its refractory period is less than one time unit and that a network is monostable or bistable when its refractory period is longer than two time units. An oscillatory network, on the other hand, is always realized if the network has a feedback mechanism which decreases the excitability of neurons when high activity level is sustained.

Some results of computer simulation of randomly connected neuron networks are also presented.