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DC Field | Value | Language |
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dc.contributor.author | DUMORTIER, Freddy | - |
dc.contributor.author | IBANEZ MESA, Santiago | - |
dc.contributor.author | Kobubu, H. | - |
dc.date.accessioned | 2007-06-01T11:24:30Z | - |
dc.date.available | 2007-06-01T11:24:30Z | - |
dc.date.issued | 2006 | - |
dc.identifier.citation | NONLINEARITY, 19(2). p. 305-328 | - |
dc.identifier.issn | 0951-7715 | - |
dc.identifier.uri | http://hdl.handle.net/1942/1564 | - |
dc.description.abstract | The 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.iso | en | - |
dc.publisher | Institute Of Physics | - |
dc.subject.other | KURAMOTO-SIVASHINSKY EQUATION; NILPOTENT SINGULARITY; STEADY SOLUTIONS;; SADDLE-FOCUS; CODIMENSION-3; ORBITS; WAVES; R-3 | - |
dc.title | Cocoon bifurcation in three-dimensional reversible vector fields | - |
dc.type | Journal Contribution | - |
dc.identifier.epage | 328 | - |
dc.identifier.issue | 2 | - |
dc.identifier.spage | 305 | - |
dc.identifier.volume | 19 | - |
local.bibliographicCitation.jcat | A1 | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.bibliographicCitation.oldjcat | A1 | - |
dc.identifier.doi | 10.1088/0951-7715/19/2/004 | - |
dc.identifier.isi | 000235461400004 | - |
item.contributor | DUMORTIER, Freddy | - |
item.contributor | IBANEZ MESA, Santiago | - |
item.contributor | Kobubu, H. | - |
item.accessRights | Closed Access | - |
item.fullcitation | DUMORTIER, Freddy; IBANEZ MESA, Santiago & Kobubu, H. (2006) Cocoon bifurcation in three-dimensional reversible vector fields. In: NONLINEARITY, 19(2). p. 305-328. | - |
item.validation | ecoom 2007 | - |
item.fulltext | No Fulltext | - |
crisitem.journal.issn | 0951-7715 | - |
crisitem.journal.eissn | 1361-6544 | - |
Appears in Collections: | Research publications |
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