Metastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics
AuthorsBressloff, Paul C.
KAUST Grant NumberKUK-C1-013-4
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AbstractWe 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.
CitationBressloff PC (2010) Metastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics. Phys Rev E 82. Available: http://dx.doi.org/10.1103/PhysRevE.82.051903.
SponsorsThis 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.
PublisherAmerican Physical Society (APS)
JournalPhysical Review E
CollectionsPublications Acknowledging KAUST Support
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