Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/20672
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dc.contributor.authorDE MAESSCHALCK, Peter-
dc.contributor.authorKUTAFINA, Ekaterina-
dc.contributor.authorPopovic, N.-
dc.date.accessioned2016-02-17T10:28:11Z-
dc.date.available2016-02-17T10:28:11Z-
dc.date.issued2016-
dc.identifier.citationAPPLIED MATHEMATICS AND COMPUTATION, 273, p. 337-352-
dc.identifier.issn0096-3003-
dc.identifier.urihttp://hdl.handle.net/1942/20672-
dc.description.abstractWe consider a three-dimensional three-time-scale system that was first proposed by Krupa et al. (2008) under the additional assumption that two singular perturbation parameters are present in the equations. While the presence of three scales was shown to give use to canard induced periodic mixed mode oscillations (MMOs) (Desroches et al., 2012) in the parameter regime studied by Krupa et al. (2008,) we additionally observe mixed mode patterns that display delayed-Hopf-type behaviour (Neishtadt, 1987). We present analytical and numerical evidence for the occurrence of stable periodic dynamics that realises both mechanisms, and we discuss the transition between them. To the best of our knowledge, the resulting mixed sector-delayed-Hopf-type MMO trajectories represent a novel class of mixed-mode dynamics in singularly perturbed systems of ordinary differential equations. (C) 2015 Elsevier Inc. All rights reserved.-
dc.description.sponsorshipThe authors' research was supported by the Research Foundation Flanders (FWO) under Grant number G.0939.10N. Moreover, E.K. acknowledges support from the Polish Ministry of Science and Higher Education. Finally, the authors thank three anonymous reviewers whose comments and suggestions greatly improved the original manuscript.-
dc.language.isoen-
dc.publisherELSEVIER SCIENCE INC-
dc.rights© 2015 Elsevier Inc. All rights reserved.-
dc.subject.othermixed-mode oscillations; delayed Hopf bifurcation; canards; neuronal modelling; fast-slow dynamics; singular perturbations-
dc.subject.otherMixed-mode oscillations; Delayed Hopf bifurcation; Canards; Neuronal modelling; Fast-slow dynamics; Singular perturbations-
dc.titleSector-delayed-Hopf-type mixed-mode oscillations in a prototypical three-time-scale model-
dc.typeJournal Contribution-
dc.identifier.epage352-
dc.identifier.spage337-
dc.identifier.volume273-
local.format.pages16-
local.bibliographicCitation.jcatA1-
dc.description.notes[De Maesschalck, P.] Hasselt Univ, B-3590 Diepenbeek, Belgium. [Kutafina, E.] AGH Univ Sci & Technol, PL-30059 Krakow, Poland. [Kutafina, E.] Uniklin RWTH Aachen, Dept Med Informat, D-52057 Aachen, Germany. [Popovic, N.] Univ Edinburgh, Sch Math, Edinburgh EH9 3FD, Midlothian, Scotland. [Popovic, N.] Univ Edinburgh, Maxwell Inst Math Sci, Edinburgh EH9 3FD, Midlothian, Scotland.-
local.publisher.placeNEW YORK-
local.type.refereedRefereed-
local.type.specifiedArticle-
dc.identifier.doi10.1016/j.amc.2015.09.083-
dc.identifier.isi000365613400031-
item.fulltextWith Fulltext-
item.accessRightsRestricted Access-
item.contributorKUTAFINA, Ekaterina-
item.contributorPopovic, N.-
item.contributorDE MAESSCHALCK, Peter-
item.fullcitationDE MAESSCHALCK, Peter; KUTAFINA, Ekaterina & Popovic, N. (2016) Sector-delayed-Hopf-type mixed-mode oscillations in a prototypical three-time-scale model. In: APPLIED MATHEMATICS AND COMPUTATION, 273, p. 337-352.-
item.validationecoom 2016-
crisitem.journal.issn0096-3003-
crisitem.journal.eissn1873-5649-
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