Master-equation approach to stochastic neurodynamics.

A Master equation approach to the stochastic neurodynamics proposed by Cowan[ in Advances in Neural Information Processing Systems 3, edited by R.P. Lippman, J.E. Moody, and D.S. Touretzky (Morgan Kaufmann, San Mateo, 1991), p.62] is investigated in this paper. We deal with a model neural network which is composed of two-state neurons obeying elementary stochastic transition rates. We show that such an approach yields concise expressions for multi-point moments and an equation of motion. We apply the formalism to an (1+1)-dimensional system. Exact and approximate expressions for various statistical parameters are obtained and compared with Monte Carlo simulations.