Repository logo
 
Publication

Torus-breakdown near a heteroclinic attractor: a case study

2021Journal article Restricted access
Simple item page
dc.contributor.authorCastro, Luísa
dc.contributor.authorRodrigues, Alexandre
dc.date.accessioned2021-09-23T11:10:42Z
dc.date.available2021-09-23T11:10:42Z
dc.date.issued2021
dc.description.abstractThere are few explicit examples in the literature of vector fields exhibiting observable chaos that may be proved analytically. This paper reports numerical experiments performed for an explicit two-parameter family of SO(2)⊕Z2𝕊𝕆(2)⊕ℤ2-symmetric vector fields whose organizing center exhibits an attracting heteroclinic network linking two saddle-foci. Each vector field in the family is the restriction to S3𝕊3 of a polynomial vector field in R4ℝ4. We investigate global bifurcations due to symmetry-breaking and we detect strange attractors via a mechanism called Torus-Breakdown. We explain how an attracting torus gets destroyed by following the changes in the unstable manifold of a saddle-focus. Although a complete understanding of the corresponding bifurcation diagram and the mechanisms underlying the dynamical changes is out of reach, we uncover complex patterns for the symmetric family under analysis, using a combination of theoretical tools and computer simulations. This article suggests a route to obtain rotational horseshoes and strange attractors; additionally, we make an attempt to elucidate some of the bifurcations involved in an Arnold tongue.pt_PT
dc.description.versioninfo:eu-repo/semantics/publishedVersionpt_PT
dc.identifier.citationCastro, L., & Rodrigues, A. (2021). Torus-Breakdown Near a Heteroclinic Attractor: A Case Study. International Journal of Bifurcation and Chaos, 31(10), 2130029. https://doi.org/10.1142/s0218127421300299pt_PT
dc.identifier.doi10.1142/S0218127421300299pt_PT
dc.identifier.issn1793-6551
dc.identifier.urihttp://hdl.handle.net/10400.22/18504
dc.language.isoengpt_PT
dc.peerreviewedyespt_PT
dc.publisherWorld Scientificpt_PT
dc.relation.publisherversionhttps://www.worldscientific.com/doi/abs/10.1142/S0218127421300299pt_PT
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/pt_PT
dc.subjectGlobal bifurcationpt_PT
dc.subjectHeteroclinic attractorpt_PT
dc.subjectArnold tonguept_PT
dc.subjectTorus-breakdownpt_PT
dc.subjectStrange attractorpt_PT
dc.subjectSymmetry-breakingpt_PT
dc.titleTorus-breakdown near a heteroclinic attractor: a case studypt_PT
dc.typejournal article
dspace.entity.typePublication
oaire.citation.endPage20pt_PT
oaire.citation.startPage1pt_PT
oaire.citation.titleInternational Journal of Bifurcation and Chaospt_PT
oaire.citation.volume31pt_PT
person.familyNameCastro Guedes
person.givenNameMaria Luísa
person.identifier.ciencia-id7D19-EABE-CF3B
person.identifier.orcid0000-0002-1312-0154
rcaap.rightsclosedAccesspt_PT
rcaap.typearticlept_PT
relation.isAuthorOfPublication59f421de-a393-47e4-83b1-fb436c35b797
relation.isAuthorOfPublication.latestForDiscovery59f421de-a393-47e4-83b1-fb436c35b797

Files

Original bundle
Now showing 1 - 1 of 1
No Thumbnail Available
Name:
ART_Luísa Castro 4.pdf
Size:
2.87 MB
Format:
Adobe Portable Document Format
Download

Collections

ESS - BBB - Artigos