Show simple item record

dc.contributor.authorAshwin, Peteren_GB
dc.contributor.authorBurylko, Oleksandren_GB
dc.contributor.authorMaistrenko, Yurien_GB
dc.contributor.departmentUniversity of Exeter; National Academy of Sciences of Ukraine; Research Centre Jülich, Germanyen_GB
dc.date.accessioned2008-03-19T12:04:17Zen_GB
dc.date.accessioned2011-01-25T10:33:29Zen_GB
dc.date.accessioned2013-03-20T12:30:55Z
dc.date.issued2008en_GB
dc.description.abstractWe study the bifurcation and dynamical behaviour of the system of N globally coupled identical phase oscillators introduced by Hansel, Mato and Meunier, in the cases N=3 and N=4. This model has been found to exhibit robust ‘slow switching’ oscillations that are caused by the presence of robust heteroclinic attractors. This paper presents a bifurcation analysis of the system in an attempt to better understand the creation of such attractors. We consider bifurcations that occur in a system of identical oscillators on varying the parameters in the coupling function. These bifurcations preserve the permutation symmetry of the system. We then investigate the implications of these bifurcations for the sensitivity to detuning (i.e. the size of the smallest perturbations that give rise to loss of frequency locking). For N=3 we find three types of heteroclinic bifurcation that are codimension-one with symmetry. On varying two parameters in the coupling function we find three curves giving (a) an S3-transcritical homoclinic bifurcation, (b) a saddle–node/heteroclinic bifurcation and (c) a Z3-heteroclinic bifurcation. We also identify several global bifurcations with symmetry that organize the bifurcation diagram; these are codimension-two with symmetry. For N=4 oscillators we determine many (but not all) codimension-one bifurcations with symmetry, including those that lead to a robust heteroclinic cycle. A robust heteroclinic cycle is stable in an open region of parameter space and unstable in another open region. Furthermore, we verify that there is a subregion where the heteroclinic cycle is the only attractor of the system, while for other parts of the phase plane it can coexist with stable limit cycles. We finish with a discussion of bifurcations that appear for this coupling function and general N, as well as for more general coupling functions.en_GB
dc.identifier.citation237 (4), pp. 454-466en_GB
dc.identifier.doi10.1016/j.physd.2007.09.015en_GB
dc.identifier.urihttp://hdl.handle.net/10036/21132en_GB
dc.language.isoenen_GB
dc.publisherElsevieren_GB
dc.relation.urlhttp://dx.doi.org/10.1016/j.physd.2007.09.015en_GB
dc.subjectcoupled phase oscillatoren_GB
dc.subjectbifurcationen_GB
dc.subjectheteroclinic cycleen_GB
dc.titleBifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillatorsen_GB
dc.typeArticleen_GB
dc.date.available2008-03-19T12:04:17Zen_GB
dc.date.available2011-01-25T10:33:29Zen_GB
dc.date.available2013-03-20T12:30:55Z
dc.identifier.issn0167-2789en_GB
dc.descriptionCopyright © 2008 Elsevier. NOTICE: This is the author’s version of a work accepted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Physica D, Vol 237, Issue 4, 2008, DOI: 10.1016/j.physd.2007.09.015en_GB
dc.identifier.journalPhysica Den_GB


Files in this item

This item appears in the following Collection(s)

Show simple item record