Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/15206
Full metadata record
DC FieldValueLanguage
dc.contributor.authorDUMORTIER, Freddy-
dc.contributor.authorIBANEZ MESA, Santiago-
dc.contributor.authorKokubu, Hiroshi-
dc.contributor.authorSimo, Carles-
dc.date.accessioned2013-06-05T12:00:50Z-
dc.date.available2013-06-05T12:00:50Z-
dc.date.issued2013-
dc.identifier.citationDISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 33 (10), p. 4435-4471-
dc.identifier.issn1078-0947-
dc.identifier.urihttp://hdl.handle.net/1942/15206-
dc.description.abstractWe study arbitrary generic unfoldings of a Hopf-zero singularity of codimension two. They can be written in the following normal form: {x' = -y + mu x - axz + A(x,y,z,lambda,mu) y' = x + mu y - ayz + B(x,y,z,lambda,mu) z' = z(2) vertical bar lambda vertical bar b(x(2) vertical bar y(2)) vertical bar C(x,y,z,lambda,mu), with a > 0, b > 0 and where A, B, C are C-infinity or C-omega functions of order O(vertical bar vertical bar(x,y,z,lambda,mu)vertical bar vertical bar(3)). Despite that the existence of Shilnikov homoclinic orbits in unfoldings of Hopf-zero singularities has been discussed previously in the literature, no result valid for arbitrary generic unfoldings is available. In this paper we present new techniques to study global bifurcations from Hopf-zero singularities. They allow us to obtain a general criterion for the existence of Shilnikov homoclinic bifurcations and also provide a detailed description of the bifurcation set. Criteria for the existence of Bykov cycles are also provided. Main tools are a blow-up method, including a related invariant theory, and a novel approach to the splitting functions of the invariant manifolds. Theoretical results are applied to the Michelson system and also to the so called extended Michelson system. Paper includes thorough numerical explorations of dynamics for both systems.-
dc.language.isoen-
dc.publisherAMER INST MATHEMATICAL SCIENCES-
dc.subject.otherHopf-zero singularities; Shilnikov homoclinic orbits; Bykov cycles; splitting functions; Michelson system-
dc.subject.otherMathematics, Applied; Mathematics-
dc.titleABOUT THE UNFOLDING OF A HOPF-ZERO SINGULARITY-
dc.typeJournal Contribution-
dc.identifier.epage4471-
dc.identifier.issue10-
dc.identifier.spage4435-
dc.identifier.volume33-
local.format.pages37-
local.bibliographicCitation.jcatA1-
dc.description.notesUniv Hasselt, B-3590 Diepenbeek, Belgium. Univ Oviedo, Dept Matemat, Oviedo 33007, Spain. Kyoto Univ, Dept Math JST CREST, Kyoto 6068502, Japan. Univ Barcelona, Dept Matemat Aplicada & Anal, Barcelona 08071, Spain.-
local.publisher.placeSPRINGFIELD-
local.type.refereedRefereed-
local.type.specifiedArticle-
dc.identifier.doi10.3934/dcds.2013.33.4435-
dc.identifier.isi000317953500005-
item.fulltextNo Fulltext-
item.accessRightsClosed Access-
item.contributorKokubu, Hiroshi-
item.contributorIBANEZ MESA, Santiago-
item.contributorDUMORTIER, Freddy-
item.contributorSimo, Carles-
item.fullcitationDUMORTIER, Freddy; IBANEZ MESA, Santiago; Kokubu, Hiroshi & Simo, Carles (2013) ABOUT THE UNFOLDING OF A HOPF-ZERO SINGULARITY. In: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 33 (10), p. 4435-4471.-
item.validationecoom 2014-
crisitem.journal.issn1078-0947-
crisitem.journal.eissn1553-5231-
Appears in Collections:Research publications
Show simple item record

SCOPUSTM   
Citations

24
checked on Sep 3, 2020

WEB OF SCIENCETM
Citations

27
checked on Jun 29, 2022

Page view(s)

48
checked on Jun 14, 2022

Google ScholarTM

Check

Altmetric


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