Dynamics of moments of FitzHugh-Nagumo neuronal models and stochastic bifurcations - art. no. 031911

For the study of the behavior of noisy neuronal models, Rodriguez and Tuckw ell have introduced an elegant and systematic method which consists of repl acing the system of stochastic differential equations with a system of dete rministic equations representing the dynamics of the means, variances, and covariance of the state variables [R. Rodriguez and H.C. Tuckwell, Phys. Re v. E 54, 5585 (1996)]. In this work, we first report a modification of thei r method in the case of the FitzHugh-Nagumo model which enhances the accura cy of the approximation without including higher order moments. This method is then combined with a self-consistency argument in order to better chara cterize the behavior of the underlying stochastic processes through the com putation of approximate auto- and cross-correlation functions of the state variables. Finally, we argue that the moments' equations can also reveal th e existence of stochastic bifurcations, i.e., qualitative changes in the dy namics of stochastic systems.