title: Metastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics.
abstract: We analyze a stochastic model of neuronal population dynamics with intrinsic noise. In the thermodynamic limit N→∞ , where N determines the size of each population, the dynamics is described by deterministic Wilson-Cowan equations. On the other hand, for finite N the dynamics is described by a master equation that determines the probability of spiking activity within each population. We first consider a single excitatory population that exhibits bistability in the deterministic limit. The steady-state probability distribution of the stochastic network has maxima at points corresponding to the stable fixed points of the deterministic network; the relative weighting of the two maxima depends on the system size. For large but finite N , we calculate the exponentially small rate of noise-induced transitions between the resulting metastable states using a Wentzel-Kramers-Brillouin (WKB) approximation and matched asymptotic expansions. We then consider a two-population excitatory or inhibitory network that supports limit cycle oscillations. Using a diffusion approximation, we reduce the dynamics to a neural Langevin equation, and show how the intrinsic noise amplifies subthreshold oscillations (quasicycles).
authors.affiliation: Mathematical Institute, University of Oxford, 24-29 St. Giles', Oxford OX1 3LB, United Kingdom.
authors.forename: Paul C
authors.initials: PC
authors.lastname: Bressloff
mesh_terms: D008390:Markov Chains; D008954:Models, Biological; D009474:Neurons / Q000378:metabolism*