Stochastic neurodynamics and the system size expansion

We present here a method for the study of stochastic neurodynamics in the master equation framework. Our aim is to obtain a statistical description of the dynamics of fluctuations and correlations of neural activity in large neural networks. We focus on a macroscopic description of the network via a master equation for the number of active neurons in the network. We present a systematic expansion of this equation using the “system size expansion”. We obtain coupled dynamical equations for the average activity and of fluctuations around this average. These equations exhibit non-monotonic approaches to equilibrium, as seen in Monte Carlo simulations.