Two-Dimensional Bumps in Piecewise Smooth Neural Fields with Synaptic Depression

Handle URI:
http://hdl.handle.net/10754/599851
Title:
Two-Dimensional Bumps in Piecewise Smooth Neural Fields with Synaptic Depression
Authors:
Bressloff, Paul C.; Kilpatrick, Zachary P.
Abstract:
We analyze radially symmetric bumps in a two-dimensional piecewise-smooth neural field model with synaptic depression. The continuum dynamics is described in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synaptic weights between populations of neurons whose mean firing rate is taken to be a Heaviside function of local activity. Synaptic depression dynamically reduces the strength of synaptic weights in response to increases in activity. We show that in the case of a Mexican hat weight distribution, sufficiently strong synaptic depression can destabilize a stationary bump solution that would be stable in the absence of depression. Numerically it is found that the resulting instability leads to the formation of a traveling spot. The local stability of a bump is determined by solutions to a system of pseudolinear equations that take into account the sign of perturbations around the circular bump boundary. © 2011 Society for Industrial and Applied Mathematics.
Citation:
Bressloff PC, Kilpatrick ZP (2011) Two-Dimensional Bumps in Piecewise Smooth Neural Fields with Synaptic Depression. SIAM Journal on Applied Mathematics 71: 379–408. Available: http://dx.doi.org/10.1137/100799423.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Applied Mathematics
KAUST Grant Number:
KUK-C1-013-4
Issue Date:
Jan-2011
DOI:
10.1137/100799423
Type:
Article
ISSN:
0036-1399; 1095-712X
Sponsors:
This publication was based on work supported in partby the National Science Foundation (DMS-0813677) and by award KUK-C1-013-4 made by KingAbdullah University of Science and Technology (KAUST).
Appears in Collections:
Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorBressloff, Paul C.en
dc.contributor.authorKilpatrick, Zachary P.en
dc.date.accessioned2016-02-28T06:42:53Zen
dc.date.available2016-02-28T06:42:53Zen
dc.date.issued2011-01en
dc.identifier.citationBressloff PC, Kilpatrick ZP (2011) Two-Dimensional Bumps in Piecewise Smooth Neural Fields with Synaptic Depression. SIAM Journal on Applied Mathematics 71: 379–408. Available: http://dx.doi.org/10.1137/100799423.en
dc.identifier.issn0036-1399en
dc.identifier.issn1095-712Xen
dc.identifier.doi10.1137/100799423en
dc.identifier.urihttp://hdl.handle.net/10754/599851en
dc.description.abstractWe analyze radially symmetric bumps in a two-dimensional piecewise-smooth neural field model with synaptic depression. The continuum dynamics is described in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synaptic weights between populations of neurons whose mean firing rate is taken to be a Heaviside function of local activity. Synaptic depression dynamically reduces the strength of synaptic weights in response to increases in activity. We show that in the case of a Mexican hat weight distribution, sufficiently strong synaptic depression can destabilize a stationary bump solution that would be stable in the absence of depression. Numerically it is found that the resulting instability leads to the formation of a traveling spot. The local stability of a bump is determined by solutions to a system of pseudolinear equations that take into account the sign of perturbations around the circular bump boundary. © 2011 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThis publication was based on work supported in partby the National Science Foundation (DMS-0813677) and by award KUK-C1-013-4 made by KingAbdullah University of Science and Technology (KAUST).en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectNeural fieldsen
dc.subjectPiecewise-smooth dynamicsen
dc.subjectSynaptic depressionen
dc.titleTwo-Dimensional Bumps in Piecewise Smooth Neural Fields with Synaptic Depressionen
dc.typeArticleen
dc.identifier.journalSIAM Journal on Applied Mathematicsen
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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