Handle URI:
http://hdl.handle.net/10754/598374
Title:
Front Propagation in Stochastic Neural Fields
Authors:
Bressloff, Paul C.; Webber, Matthew A.
Abstract:
We analyze the effects of extrinsic multiplicative noise on front propagation in a scalar neural field with excitatory connections. Using a separation of time scales, we represent the fluctuating front in terms of a diffusive-like displacement (wandering) of the front from its uniformly translating position at long time scales, and fluctuations in the front profile around its instantaneous position at short time scales. One major result of our analysis is a comparison between freely propagating fronts and fronts locked to an externally moving stimulus. We show that the latter are much more robust to noise, since the stochastic wandering of the mean front profile is described by an Ornstein-Uhlenbeck process rather than a Wiener process, so that the variance in front position saturates in the long time limit rather than increasing linearly with time. Finally, we consider a stochastic neural field that supports a pulled front in the deterministic limit, and show that the wandering of such a front is now subdiffusive. © 2012 Society for Industrial and Applied Mathematics.
Citation:
Bressloff PC, Webber MA (2012) Front Propagation in Stochastic Neural Fields. SIAM J Appl Dyn Syst 11: 708–740. Available: http://dx.doi.org/10.1137/110851031.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Applied Dynamical Systems
KAUST Grant Number:
KUK-C1-013-04
Issue Date:
Jan-2012
DOI:
10.1137/110851031
Type:
Article
ISSN:
1536-0040
Sponsors:
This publication was based on work supported in part by the National Science Foundation (DMS-1120327), the King Abdullah University of Science and Technology (award KUK-C1-013-04), and the Systems Biology Doctoral Training Centre, University of Oxford. We are also grateful for access to the Oxford Supercomputing Center.
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Full metadata record

DC FieldValue Language
dc.contributor.authorBressloff, Paul C.en
dc.contributor.authorWebber, Matthew A.en
dc.date.accessioned2016-02-25T13:19:37Zen
dc.date.available2016-02-25T13:19:37Zen
dc.date.issued2012-01en
dc.identifier.citationBressloff PC, Webber MA (2012) Front Propagation in Stochastic Neural Fields. SIAM J Appl Dyn Syst 11: 708–740. Available: http://dx.doi.org/10.1137/110851031.en
dc.identifier.issn1536-0040en
dc.identifier.doi10.1137/110851031en
dc.identifier.urihttp://hdl.handle.net/10754/598374en
dc.description.abstractWe analyze the effects of extrinsic multiplicative noise on front propagation in a scalar neural field with excitatory connections. Using a separation of time scales, we represent the fluctuating front in terms of a diffusive-like displacement (wandering) of the front from its uniformly translating position at long time scales, and fluctuations in the front profile around its instantaneous position at short time scales. One major result of our analysis is a comparison between freely propagating fronts and fronts locked to an externally moving stimulus. We show that the latter are much more robust to noise, since the stochastic wandering of the mean front profile is described by an Ornstein-Uhlenbeck process rather than a Wiener process, so that the variance in front position saturates in the long time limit rather than increasing linearly with time. Finally, we consider a stochastic neural field that supports a pulled front in the deterministic limit, and show that the wandering of such a front is now subdiffusive. © 2012 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThis publication was based on work supported in part by the National Science Foundation (DMS-1120327), the King Abdullah University of Science and Technology (award KUK-C1-013-04), and the Systems Biology Doctoral Training Centre, University of Oxford. We are also grateful for access to the Oxford Supercomputing Center.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectMultiplicative noiseen
dc.subjectNeural fielden
dc.subjectStimulus-lockingen
dc.subjectTraveling frontsen
dc.titleFront Propagation in Stochastic Neural Fieldsen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Applied Dynamical Systemsen
dc.contributor.institutionUniversity of Utah, Salt Lake City, United Statesen
dc.contributor.institutionUniversity of Oxford, Oxford, United Kingdomen
kaust.grant.numberKUK-C1-013-04en
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