Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/1564
Full metadata record
DC FieldValueLanguage
dc.contributor.authorDUMORTIER, Freddy-
dc.contributor.authorIBANEZ MESA, Santiago-
dc.contributor.authorKobubu, H.-
dc.date.accessioned2007-06-01T11:24:30Z-
dc.date.available2007-06-01T11:24:30Z-
dc.date.issued2006-
dc.identifier.citationNONLINEARITY, 19(2). p. 305-328-
dc.identifier.issn0951-7715-
dc.identifier.urihttp://hdl.handle.net/1942/1564-
dc.description.abstractThe cocoon bifurcation is a set of rich bifurcation phenomena numerically observed by Lau (1992 Int. J. Bifurc. Chaos 2 543-58) in the Michelson system, a three-dimensional ODE system describing travelling waves of the Kuramoto-Sivashinsky equation. In this paper, we present an organizing centre of the principal part of the cocoon bifurcation in more general terms in the setting of reversible vector fields on R-3. We prove that in a generic unfolding of an organizing centre called the cusp-transverse heteroclinic chain, there is a cascade of heteroclinic bifurcations with an increasing length close to the organizing Centre, which resembles the principal part of the cocoon bifurcation. We also study a heteroclinic cycle called the reversible Bykov cycle. Such a cycle is believed to occur in the Michelson system, as well as in a model equation of a Josephson Junction (van den Berg et al 2003 Nonlinearity 16 707-17). We conjecture that a reversible Bykov cycle is, in its unfolding, an accumulation point of a sequence of cusp-transverse heteroclinic chains. As a first result in this direction, we show that a reversible Bykov cycle is an accumulation point of reversible generic saddle-node bifurcations of periodic orbits, the main ingredient of the cusp-transverse heteroclinic chain.-
dc.language.isoen-
dc.publisherInstitute Of Physics-
dc.subject.otherKURAMOTO-SIVASHINSKY EQUATION; NILPOTENT SINGULARITY; STEADY SOLUTIONS;; SADDLE-FOCUS; CODIMENSION-3; ORBITS; WAVES; R-3-
dc.titleCocoon bifurcation in three-dimensional reversible vector fields-
dc.typeJournal Contribution-
dc.identifier.epage328-
dc.identifier.issue2-
dc.identifier.spage305-
dc.identifier.volume19-
local.bibliographicCitation.jcatA1-
local.type.refereedRefereed-
local.type.specifiedArticle-
dc.bibliographicCitation.oldjcatA1-
dc.identifier.doi10.1088/0951-7715/19/2/004-
dc.identifier.isi000235461400004-
item.fulltextNo Fulltext-
item.validationecoom 2007-
item.contributorKobubu, H.-
item.contributorIBANEZ MESA, Santiago-
item.contributorDUMORTIER, Freddy-
item.fullcitationDUMORTIER, Freddy; IBANEZ MESA, Santiago & Kobubu, H. (2006) Cocoon bifurcation in three-dimensional reversible vector fields. In: NONLINEARITY, 19(2). p. 305-328.-
item.accessRightsClosed Access-
crisitem.journal.issn0951-7715-
crisitem.journal.eissn1361-6544-
Appears in Collections:Research publications
Show simple item record

SCOPUSTM   
Citations

23
checked on Sep 3, 2020

WEB OF SCIENCETM
Citations

26
checked on Jun 29, 2022

Page view(s)

42
checked on Jun 14, 2022

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.