STATISTICAL PROPERTIES OF STOCHASTIC NONLINEAR DYNAMICAL MODELS OF SINGLE SPIKING NEURONS AND NEURAL NETWORKS

Dynamical stochastic models of single neurons and neural networks ofte n take the form of a system of n greater than or equal to 2 coupled st ochastic differential equations. We consider such systems under the as sumption that third and higher order central moments are relatively sm all. In the general case, a system of 1/2n(n+3) (generally) nonlinear coupled ordinary differential equations holds for the approximate mean s; variances, and covariances. For the general linear system the solut ions of these equations give exact results-this is illustrated in a si mple case. Generally, the moment equations can be solved numerically. Results are given for a spiking Fitzhugh-Nagumo model neuron driven by a current with additive white noise. Differential equations are obtai ned for the means, variances, and covariances of the dynamical variabl es in a network of n connected spiking neurons in the presence of nois e.