Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/18093
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dc.contributor.authorDE MAESSCHALCK, Peter-
dc.contributor.authorRebollo-Perdomo, S.-
dc.contributor.authorTorregrosa, J.-
dc.date.accessioned2015-01-13T09:34:38Z-
dc.date.available2015-01-13T09:34:38Z-
dc.date.issued2015-
dc.identifier.citationJOURNAL OF DIFFERENTIAL EQUATIONS, 258 (2), p. 588-620-
dc.identifier.issn0022-0396-
dc.identifier.urihttp://hdl.handle.net/1942/18093-
dc.description.abstractThis paper concerns the study of small-amplitude limit cycles that appear in the phase portrait near an unfolded fake saddle singularity. This degenerate singularity is also known as an impassable grain. The canonical form of the unperturbed vector field is like a degenerate flow box. Near the singularity, the phase portrait consists of parallel fibers, all but one of which have no singular points, and at the singular fiber, there is one node. We demonstrate different techniques in order to show that the cyclicity is bigger than or equal to two when the canonical form is quadratic. (C) 2014 Elsevier Inc. All rights reserved.-
dc.description.sponsorshipThe first author acknowledges the support of FWO Vlaanderen (Grant number G093910). The third author was supported by the MINECO/FEDER MTM2008-03437, MTM2013-40998-P and UNAB10-4E-378 grants, by the AGAUR 2014SGR568 grant, and by the European Community FP7-PEOPLE-2012-IRSES-316338 and by the FP7-PEOPLE-2012-IRSES-318999 grants. We thank Jorge Galan for numerical simulations confirming the existence of a homoclinic connection.-
dc.language.isoen-
dc.publisherACADEMIC PRESS INC ELSEVIER SCIENCE-
dc.rights© 2014 Elsevier Inc. All rights reserved.-
dc.subject.othercyclicity; fake saddle; impassable grain; limit cycle; bifurcation; singularity unfolding-
dc.subject.otherCyclicity; Fake saddle; Impassable grain; Limit cycle; Bifurcation; Singularity unfolding-
dc.titleCyclicity of a fake saddle inside the quadratic vector fields-
dc.typeJournal Contribution-
dc.identifier.epage620-
dc.identifier.issue2-
dc.identifier.spage588-
dc.identifier.volume258-
local.format.pages33-
local.bibliographicCitation.jcatA1-
dc.description.notes[De Maesschalck, P.] Hasselt Univ, B-3500 Hasselt, Belgium. [Rebollo-Perdomo, S.] Ctr Recerca Matemat, Barcelona 08193, Spain. [Torregrosa, J.] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Spain.-
local.publisher.placeSAN DIEGO-
local.type.refereedRefereed-
local.type.specifiedArticle-
dc.identifier.doi10.1016/j.jde.2014.09.024-
dc.identifier.isi000345488200013-
item.accessRightsOpen Access-
item.fullcitationDE MAESSCHALCK, Peter; Rebollo-Perdomo, S. & Torregrosa, J. (2015) Cyclicity of a fake saddle inside the quadratic vector fields. In: JOURNAL OF DIFFERENTIAL EQUATIONS, 258 (2), p. 588-620.-
item.contributorDE MAESSCHALCK, Peter-
item.contributorRebollo-Perdomo, S.-
item.contributorTorregrosa, J.-
item.fulltextWith Fulltext-
item.validationecoom 2015-
crisitem.journal.issn0022-0396-
crisitem.journal.eissn1090-2732-
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