A dynamical system for the approximate moments of nonlinear stochastic models of spiking neurons and networks

We consider multidimensional systems of coupled nonlinear stochastic differential equations suitable for the study of the dynamics of collections of interacting noisy spiking neurons. Assumptions based on the smallness of third and higher central order moments of membrane potentials and recovery variables are used to derive a system of ordinary differential equations for the approximate means, variances, and covariances. We show the usefulness of such a derivation for different cases of model neurons under the action of white noise currents.