Properties of Neuronal Model Dependence in the Randomly and Symmetrically Connected Neural Networks

Abstract

A large number of equilibrium states or fixed points is in a randomly and symmetrically connected neural network. Recently it has been shown that the maximum number which can be realized depend on the model of the single neuron. Here we show some network properites of the neuronal model dependence which include the maximum number of equibrium states and the activity of these states. Furthermore, the invariant activity in each model is also derived, where the activity does not depend on the statistical parameters designated by the probability distribution of connection weights between neurons and a threshold of neurons.