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dc.contributor.authorPérez-Cervera, A
dc.contributor.authorAshwin, P
dc.contributor.authorHuguet, G
dc.contributor.authorM-Seara, T
dc.contributor.authorRankin, J
dc.date.accessioned2019-07-05T13:27:59Z
dc.date.issued2019-08-05
dc.description.abstractWe study the dynamics arising when two identical oscillators are coupled near a Hopf bifurcation where we assume a parameter ε uncouples the system at ε = 0. Using a normal form for N = 2 identical systems undergoing Hopf bifurcation, we explore the dynamical properties. Matching the normal form coefficients to a coupled Wilson-Cowan oscillator network gives an understanding of different types of behaviour that arise in a model of perceptual bistability. Notably, we find bistability between in-phase and anti-phase solutions that demonstrates the feasibility for synchronisation to act as the mechanism by which periodic inputs can be segregated (rather than via strong inhibitory coupling, as in existing models). Using numerical continuation we confirm our theoretical analysis for small coupling strength and explore the bifurcation diagrams for large coupling strength, where the normal form approximation breaks down.en_GB
dc.description.sponsorshipEngineering and Physical Sciences Research Council (EPSRC)en_GB
dc.description.sponsorshipRussian Scientific Foundationen_GB
dc.identifier.citationVol. 9 (7). Published online 05 August 2019.en_GB
dc.identifier.doi10.1186/s13408-019-0075-2
dc.identifier.grantnumberEP/N014391/1en_GB
dc.identifier.grantnumberMTM2015-65715-Pen_GB
dc.identifier.grantnumberMINECO-FEDER-UE MTM-2015-71509-C2-2-Ren_GB
dc.identifier.grantnumber2017SGR1049en_GB
dc.identifier.grantnumber14-41-00044en_GB
dc.identifier.grantnumberRYC-2014-15866en_GB
dc.identifier.grantnumberMINECO-FEDER-UE MTM2012-31714en_GB
dc.identifier.urihttp://hdl.handle.net/10871/37864
dc.language.isoenen_GB
dc.publisherSpringeren_GB
dc.rights© The Author(s) 2019. Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
dc.subjectSynchronyen_GB
dc.subjectPerceptual Bistablityen_GB
dc.subjectBifurcation Analysisen_GB
dc.subjectNormal Formen_GB
dc.subjectNeural Competitionen_GB
dc.subjectHopf Bifurcationen_GB
dc.titleThe uncoupling limit of identical Hopf bifurcations with an application to perceptual bistabilityen_GB
dc.typeArticleen_GB
dc.date.available2019-07-05T13:27:59Z
dc.identifier.issn2190-8567
dc.descriptionThis is the final version. Available from Springer via the DOI in this record.en_GB
dc.identifier.journalJournal of Mathematical Neuroscienceen_GB
dc.rights.urihttp://www.rioxx.net/licenses/all-rights-reserveden_GB
dcterms.dateAccepted2019-06-19
exeter.funder::Engineering and Physical Sciences Research Council (EPSRC)en_GB
rioxxterms.versionVoRen_GB
rioxxterms.licenseref.startdate2019-06-19
rioxxterms.typeJournal Article/Reviewen_GB
refterms.dateFCD2019-07-05T10:19:57Z
refterms.versionFCDAM
refterms.panelBen_GB


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