Stochastic Dynamics of Three--State Neural Networks

We present here an analysis of the stochastic neurodynamics of a neural network composed of three--state neurons described by a master equation. An outer--product representation of the master equation is employed. In this representation, an extension of the analysis from two to three--state neurons is easily performed. We apply this formalism with approximation schemes to a simple three--state network and compare the results with Monte Carlo simulations. 2 INTRODUCTION Studies of single neurons or networks under the influence of noise have been a continuing item in neural network modelling. In particular, the analogy with spin systems at finite temprature has produced many important results on networks of two--state neurons. However, studies of networks of three--state neurons have been rather limited (Meunier, Hansel and Verga, 1989). A master equation was introduced by Cowan (1991) to study stochastic neural networks. The equation uses the formalism of "second quantization" for clas..