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

Paul C. Bressloff

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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). © 2010 The American Physical Society.
Original languageEnglish (US)
JournalPhysical Review E
Issue number5
StatePublished - Nov 3 2010
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-4
Acknowledgements: This publication was based on work supported in part by the National Science Foundation Grant No. DMS-0813677 and by Award No. KUK-C1-013-4 by King Abdullah University of Science and Technology (KAUST). P. C. B. was also partially supported by the Royal Society Wolfson Foundation.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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