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Homoclinic and big bang bifurcations of an embedding of 1D Allee's functions into a 2D diffeomorphism

2017-08Journal article Restricted access
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dc.contributor.authorRocha, J. Leonel
dc.contributor.authorTaha, Abdel-Kaddous
dc.contributor.authorFournier-Prunaret, D.
dc.date.accessioned2019-03-19T12:21:46Z
dc.date.available2019-03-19T12:21:46Z
dc.date.issued2017-08
dc.description.abstractIn this work a thorough study is presented of the bifurcation structure of an embedding of one-dimensional Allee's functions into a two-dimensional diffeomorphism. A complete classification of the nature and stability of the fixed points, on the contour lines of the two-dimensional diffeomorphism, is provided. A necessary and sufficient condition so that the Allee fixed point is a snapback repeller is established. Sufficient conditions for the occurrence of homoclinic tangencies of a saddle fixed point of the two-dimensional diffeomorphism are also established, associated to the snapback repeller bifurcation of the endomorphism defined by the Allee functions. The main results concern homoclinic and big bang bifurcations of the diffeomorphism as "germinal" bifurcations of the Allee functions. Our results confirm previous predictions of structures of homoclinic and big bang bifurcation curves in dimension one and extend these studies to "local" concepts of Allee effect and big bang bifurcations to this two-dimensional exponential diffeomorphism.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationROCHA, Leonel; TAHA, Abdel-Kaddous; FOURNIER-PRUNARET, D. – Homoclinic and big bang bifurcations of an embedding of 1D Allee's functions into a 2D diffeomorphism. International Journal of Bifurcation and Chaos. ISSN 0218-1274. Vol. 27, N.º 9 (2017), pp. 1730030-1- 1730030-25pt_PT
dc.identifier.doi10.1142/S0218127417300300pt_PT
dc.identifier.issn0218-1274
dc.identifier.issn1793-6551
dc.identifier.urihttp://hdl.handle.net/10400.21/9738
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherWorld Scientific Publishingpt_PT
dc.relationDinâmicas e Estruturas de Bifurcação de Aplicações Logísticas Generalizadas
dc.relation.publisherversionhttps://www.worldscientific.com/doi/pdf/10.1142/S0218127417300300pt_PT
dc.subjectDiffeomorphismpt_PT
dc.subjectAllee's functionspt_PT
dc.subjectHomoclinic bifurcationspt_PT
dc.subjectBig bang bifurcationspt_PT
dc.subjectFold and flip bifurcationspt_PT
dc.subjectBifurcações homoclínicaspt_PT
dc.titleHomoclinic and big bang bifurcations of an embedding of 1D Allee's functions into a 2D diffeomorphismpt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.awardTitleDinâmicas e Estruturas de Bifurcação de Aplicações Logísticas Generalizadas
oaire.awardURIinfo:eu-repo/grantAgreement/FCT/5876/UID%2FMAT%2F00006%2F2013/PT
oaire.awardURIinfo:eu-repo/grantAgreement/FCT//SFRH%2FBSAB%2F128144%2F2016/PT
oaire.citation.endPage1730030-25pt_PT
oaire.citation.issue9pt_PT
oaire.citation.startPage1730030-1pt_PT
oaire.citation.titleInternational Journal of Bifurcation and Chaospt_PT
oaire.citation.volume27pt_PT
oaire.fundingStream5876
person.familyNameRocha
person.givenNameJ. Leonel
person.identifier1869126
person.identifier.ciencia-id6A13-4D5A-BABA
person.identifier.orcid0000-0001-8053-6822
person.identifier.scopus-author-id24829973500
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.identifierhttp://doi.org/10.13039/501100001871
project.funder.nameFundação para a Ciência e a Tecnologia
project.funder.nameFundação para a Ciência e a Tecnologia
rcaap.rightsclosedAccesspt_PT
rcaap.typearticlept_PT
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relation.isProjectOfPublication7a20a023-28f3-4511-9c17-8af40583253d
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