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

Handle URI:
http://hdl.handle.net/10754/598815
Title:
Metastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamics
Authors:
Bressloff, Paul C.
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). © 2010 The American Physical Society.
Citation:
Bressloff 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.
Publisher:
American Physical Society (APS)
Journal:
Physical Review E
KAUST Grant Number:
KUK-C1-013-4
Issue Date:
3-Nov-2010
DOI:
10.1103/PhysRevE.82.051903
PubMed ID:
21230496
Type:
Article
ISSN:
1539-3755; 1550-2376
Sponsors:
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.
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Full metadata record

DC FieldValue Language
dc.contributor.authorBressloff, Paul C.en
dc.date.accessioned2016-02-25T13:41:46Zen
dc.date.available2016-02-25T13:41:46Zen
dc.date.issued2010-11-03en
dc.identifier.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.en
dc.identifier.issn1539-3755en
dc.identifier.issn1550-2376en
dc.identifier.pmid21230496en
dc.identifier.doi10.1103/PhysRevE.82.051903en
dc.identifier.urihttp://hdl.handle.net/10754/598815en
dc.description.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.en
dc.description.sponsorshipThis 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.en
dc.publisherAmerican Physical Society (APS)en
dc.titleMetastable states and quasicycles in a stochastic Wilson-Cowan model of neuronal population dynamicsen
dc.typeArticleen
dc.identifier.journalPhysical Review Een
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
dc.contributor.institutionUniversity of Utah, Salt Lake City, United Statesen
kaust.grant.numberKUK-C1-013-4en
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