Introduction

Computer simulation has become a valuable - even indispensable - tool in the search for viable models of the self-organizing and self-replicating systems of the biological world as well as the inanimate systems of conventional physics. In this paper we shall present selected results from a large number of computer experiments on model neural networks of a very simple type. In the spirit of McCulloch & Pitts (1943) and Caianiello (1961), the model involves binary threshold elements (which may crudely represent neurons); these elements operate synchronously in discrete time. The synaptic interactions between neurons are represented by a non-symmetric coupling matrix which determines the strength of the stimulus which an arbitrary neuronal element, in the ‘on’ configuration, can exert on a second neuron to which it sends an input connection line. Within this model, the classes of networks singled out for study are defined by one or another prescription for random connection of the nodal units, implying that the entries in the coupling matrix are chosen randomly subject to certain overall constraints governing the number of inputs per ‘neuron’, the fraction of inhibitory ‘neurons’ and the magnitudes of the non-zero couplings.

We are primarily concerned with the statistics of cycling activity in such model networks, as gleaned from computer runs which follow the autonomous dynamical evolution of sample nets. An aspect of considerable interest is the stability of cyclic modes under disturbance of a single neuron in a single state of the cycle.