Binocular Rivalry in a Competitive Neural Network with Synaptic Depression

Handle URI:
http://hdl.handle.net/10754/597670
Title:
Binocular Rivalry in a Competitive Neural Network with Synaptic Depression
Authors:
Kilpatrick, Zachary P.; Bressloff, Paul C.
Abstract:
We study binocular rivalry in a competitive neural network with synaptic depression. In particular, we consider two coupled hypercolums within primary visual cortex (V1), representing orientation selective cells responding to either left or right eye inputs. Coupling between hypercolumns is dominated by inhibition, especially for neurons with dissimilar orientation preferences. Within hypercolumns, recurrent connectivity is excitatory for similar orientations and inhibitory for different orientations. All synaptic connections are modifiable by local synaptic depression. When the hypercolumns are driven by orthogonal oriented stimuli, it is possible to induce oscillations that are representative of binocular rivalry. We first analyze the occurrence of oscillations in a space-clamped version of the model using a fast-slow analys is, taking advantage of the fact that depression evolves much slower than population activity. We th en analyze the onset of oscillations in the full spatially extended system by carrying out a piecewise smooth stability analysis of single (winner-take-all) and double (fusion) bumps within the network. Although our stability analysis takes into account only instabilities associated with real eigenvalues, it identifies points of instability that are consistent with what is found numerically. In particular, we show that, in regions of parameter space where double bumps are unstable and no single bumps exist, binocular rivalry can arise as a slow alternation between either population supporting a bump. © 2010 Society for Industrial and Applied Mathematics.
Citation:
Kilpatrick ZP, Bressloff PC (2010) Binocular Rivalry in a Competitive Neural Network with Synaptic Depression. SIAM J Appl Dyn Syst 9: 1303–1347. Available: http://dx.doi.org/10.1137/100788872.
Publisher:
Society for Industrial & Applied Mathematics (SIAM)
Journal:
SIAM Journal on Applied Dynamical Systems
KAUST Grant Number:
KUK-C1-013-4
Issue Date:
Jan-2010
DOI:
10.1137/100788872
Type:
Article
ISSN:
1536-0040
Sponsors:
This research was supported in part by the National Science Foundation (DMS-0813677) and by award KUK-C1-013-4 made by King Abdullah University of Science and Technology (KAUST).The work of this author was partially supported by the Royal Society Wolfson Foundation.
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorKilpatrick, Zachary P.en
dc.contributor.authorBressloff, Paul C.en
dc.date.accessioned2016-02-25T12:44:06Zen
dc.date.available2016-02-25T12:44:06Zen
dc.date.issued2010-01en
dc.identifier.citationKilpatrick ZP, Bressloff PC (2010) Binocular Rivalry in a Competitive Neural Network with Synaptic Depression. SIAM J Appl Dyn Syst 9: 1303–1347. Available: http://dx.doi.org/10.1137/100788872.en
dc.identifier.issn1536-0040en
dc.identifier.doi10.1137/100788872en
dc.identifier.urihttp://hdl.handle.net/10754/597670en
dc.description.abstractWe study binocular rivalry in a competitive neural network with synaptic depression. In particular, we consider two coupled hypercolums within primary visual cortex (V1), representing orientation selective cells responding to either left or right eye inputs. Coupling between hypercolumns is dominated by inhibition, especially for neurons with dissimilar orientation preferences. Within hypercolumns, recurrent connectivity is excitatory for similar orientations and inhibitory for different orientations. All synaptic connections are modifiable by local synaptic depression. When the hypercolumns are driven by orthogonal oriented stimuli, it is possible to induce oscillations that are representative of binocular rivalry. We first analyze the occurrence of oscillations in a space-clamped version of the model using a fast-slow analys is, taking advantage of the fact that depression evolves much slower than population activity. We th en analyze the onset of oscillations in the full spatially extended system by carrying out a piecewise smooth stability analysis of single (winner-take-all) and double (fusion) bumps within the network. Although our stability analysis takes into account only instabilities associated with real eigenvalues, it identifies points of instability that are consistent with what is found numerically. In particular, we show that, in regions of parameter space where double bumps are unstable and no single bumps exist, binocular rivalry can arise as a slow alternation between either population supporting a bump. © 2010 Society for Industrial and Applied Mathematics.en
dc.description.sponsorshipThis research was supported in part by the National Science Foundation (DMS-0813677) and by award KUK-C1-013-4 made by King Abdullah University of Science and Technology (KAUST).The work of this author was partially supported by the Royal Society Wolfson Foundation.en
dc.publisherSociety for Industrial & Applied Mathematics (SIAM)en
dc.subjectBinocular rivalryen
dc.subjectHypercolumnen
dc.subjectNeuronal networken
dc.subjectPiecewise-smooth dynamicsen
dc.subjectSynaptic depressionen
dc.titleBinocular Rivalry in a Competitive Neural Network with Synaptic Depressionen
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-C1-013-4en
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