Partial classification of heteroclinic behaviour associated with the perturbation of hexagonal planforms
Autor(a) principal: | |
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Data de Publicação: | 2008 |
Outros Autores: | , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.7/44 |
Resumo: | Physical systems often exhibit pattern-forming instabilities. Equivariant bifurcation theory is often used to investigate the existence and stability of spatially doubly periodic solutions with respect to the hexagonal lattice. Previous studies have focused on the six- and twelve-dimensional representation of the hexagonal lattice where the symmetry of the model is perfect. Here, perturbation of group orbits of translation-free axial planforms in the six- and twelve-dimensional representations is considered. This problem is studied via the abstract action of the symmetry group of the perturbation on the group orbit of the planform. A partial classification for the behaviour of the group orbits is obtained, showing the existence of homoclinic and heteroclinic cycles between equilibria |
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Partial classification of heteroclinic behaviour associated with the perturbation of hexagonal planformsforced symmetry-breakinghexagon planformsheteroclinic cyclesPhysical systems often exhibit pattern-forming instabilities. Equivariant bifurcation theory is often used to investigate the existence and stability of spatially doubly periodic solutions with respect to the hexagonal lattice. Previous studies have focused on the six- and twelve-dimensional representation of the hexagonal lattice where the symmetry of the model is perfect. Here, perturbation of group orbits of translation-free axial planforms in the six- and twelve-dimensional representations is considered. This problem is studied via the abstract action of the symmetry group of the perturbation on the group orbit of the planform. A partial classification for the behaviour of the group orbits is obtained, showing the existence of homoclinic and heteroclinic cycles between equilibriaARCAParker, M. J.Stewart, I. N.Gomes, M. G. M.2009-10-08T13:53:37Z200820082009-10-08T13:53:37Z2008-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.7/44engParker, M. J., Stewart, I. N., Gomes, M. G. M. (2008)."Partial classification of heteroclinic behaviour associated with the perturbation of hexagonal planforms". Proceedings. Biological sciences, R.S. 269(1488):227-33info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2022-11-29T14:34:35Zoai:arca.igc.gulbenkian.pt:10400.7/44Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T16:11:32.617853Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
Partial classification of heteroclinic behaviour associated with the perturbation of hexagonal planforms |
title |
Partial classification of heteroclinic behaviour associated with the perturbation of hexagonal planforms |
spellingShingle |
Partial classification of heteroclinic behaviour associated with the perturbation of hexagonal planforms Parker, M. J. forced symmetry-breaking hexagon planforms heteroclinic cycles |
title_short |
Partial classification of heteroclinic behaviour associated with the perturbation of hexagonal planforms |
title_full |
Partial classification of heteroclinic behaviour associated with the perturbation of hexagonal planforms |
title_fullStr |
Partial classification of heteroclinic behaviour associated with the perturbation of hexagonal planforms |
title_full_unstemmed |
Partial classification of heteroclinic behaviour associated with the perturbation of hexagonal planforms |
title_sort |
Partial classification of heteroclinic behaviour associated with the perturbation of hexagonal planforms |
author |
Parker, M. J. |
author_facet |
Parker, M. J. Stewart, I. N. Gomes, M. G. M. |
author_role |
author |
author2 |
Stewart, I. N. Gomes, M. G. M. |
author2_role |
author author |
dc.contributor.none.fl_str_mv |
ARCA |
dc.contributor.author.fl_str_mv |
Parker, M. J. Stewart, I. N. Gomes, M. G. M. |
dc.subject.por.fl_str_mv |
forced symmetry-breaking hexagon planforms heteroclinic cycles |
topic |
forced symmetry-breaking hexagon planforms heteroclinic cycles |
description |
Physical systems often exhibit pattern-forming instabilities. Equivariant bifurcation theory is often used to investigate the existence and stability of spatially doubly periodic solutions with respect to the hexagonal lattice. Previous studies have focused on the six- and twelve-dimensional representation of the hexagonal lattice where the symmetry of the model is perfect. Here, perturbation of group orbits of translation-free axial planforms in the six- and twelve-dimensional representations is considered. This problem is studied via the abstract action of the symmetry group of the perturbation on the group orbit of the planform. A partial classification for the behaviour of the group orbits is obtained, showing the existence of homoclinic and heteroclinic cycles between equilibria |
publishDate |
2008 |
dc.date.none.fl_str_mv |
2008 2008 2008-01-01T00:00:00Z 2009-10-08T13:53:37Z 2009-10-08T13:53:37Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/10400.7/44 |
url |
http://hdl.handle.net/10400.7/44 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Parker, M. J., Stewart, I. N., Gomes, M. G. M. (2008)."Partial classification of heteroclinic behaviour associated with the perturbation of hexagonal planforms". Proceedings. Biological sciences, R.S. 269(1488):227-33 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799130571379572736 |