Computer Experiment on Characteristic Modes of Excitation in a Random Neural Network on the McCulloch-Pitts Model

Abstract

Numerical studies are made out the behavior of a random neural network in which each neuron is coupled to a certain number of randomly chosen neurons. Such a random-net serves as a simple model for an elemental sub-network of the cortex. Neurons are regarded as binary decision elements, and they synchronously update their values in discrete time steps according to a deterministic equation (the McCulloch-Pitts model). It is found that each random-net containing one hundred neurons has only a few kinds of characteristic modes of excitation. Periods of these modes are usually less than ten steps when the number of connections per neuron is two to five. For the random-net containing one thousand neurons, an excited mode is practically aperiodic. When the refractory period is introduced, however, a nearly periodic oscillation takes place in the activity of the network.