The Mathematical Institute, University of Oxford, Eprints Archive

Metastable states and quasicycles in a stochastic Wilson-Cowan
model of neuronal population dynamics

Bressloff, P. C. (2010) Metastable states and quasicycles in a stochastic Wilson-Cowan
model of neuronal population dynamics.
Physical Review E . (Submitted)

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Abstract

We analyze a stochastic model of neuronal population dynamics with intrinsic noise. In the thermodynamic limit N -> infinity, 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/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).

Item Type:Article
Subjects:D - G > General
Research Groups:Oxford Centre for Collaborative Applied Mathematics
ID Code:1038
Deposited By:Peter Hudston
Deposited On:07 Jan 2011 08:44
Last Modified:09 Feb 2012 15:49

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