Phase portraits and bifurcation diagram of the Gray-Scott model

We give a complete classification of the phase portraits in the Poincaré disk for the cubic polynomial systems ˙ x = 1-x-axy2, ˙ y = -by + axy2, in R2 according with the values of its two parameters a and b. These differential systems correspond to the Gray-Scott model. Moreover we provide the bifur...

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Autores: Chen, Ting|||0000-0001-6570-885X, Li, Shimin|||0000-0003-1695-0097, Llibre, Jaume|||0000-0002-9511-5999
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:236644
Acceso en línea:https://ddd.uab.cat/record/236644
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2020.124840
Access Level:acceso abierto
Palabra clave:Gray-Scott model
Cubic polynomial system
Phase portraits
Bifurcation diagram
Hopf bifurcation
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spelling Phase portraits and bifurcation diagram of the Gray-Scott modelChen, Ting|||0000-0001-6570-885XLi, Shimin|||0000-0003-1695-0097Llibre, Jaume|||0000-0002-9511-5999Gray-Scott modelCubic polynomial systemPhase portraitsBifurcation diagramHopf bifurcationWe give a complete classification of the phase portraits in the Poincaré disk for the cubic polynomial systems ˙ x = 1-x-axy2, ˙ y = -by + axy2, in R2 according with the values of its two parameters a and b. These differential systems correspond to the Gray-Scott model. Moreover we provide the bifurcation diagram in the parameter plane (a,b) of these systems. 22021-01-0120212021-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/236644https://dx.doi.org/urn:doi:10.1016/j.jmaa.2020.124840reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2016-77278-PAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617European Commission https://doi.org/10.13039/501100000780 777911open accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2366442026-06-06T12:50:31Z
dc.title.none.fl_str_mv Phase portraits and bifurcation diagram of the Gray-Scott model
title Phase portraits and bifurcation diagram of the Gray-Scott model
spellingShingle Phase portraits and bifurcation diagram of the Gray-Scott model
Chen, Ting|||0000-0001-6570-885X
Gray-Scott model
Cubic polynomial system
Phase portraits
Bifurcation diagram
Hopf bifurcation
title_short Phase portraits and bifurcation diagram of the Gray-Scott model
title_full Phase portraits and bifurcation diagram of the Gray-Scott model
title_fullStr Phase portraits and bifurcation diagram of the Gray-Scott model
title_full_unstemmed Phase portraits and bifurcation diagram of the Gray-Scott model
title_sort Phase portraits and bifurcation diagram of the Gray-Scott model
dc.creator.none.fl_str_mv Chen, Ting|||0000-0001-6570-885X
Li, Shimin|||0000-0003-1695-0097
Llibre, Jaume|||0000-0002-9511-5999
author Chen, Ting|||0000-0001-6570-885X
author_facet Chen, Ting|||0000-0001-6570-885X
Li, Shimin|||0000-0003-1695-0097
Llibre, Jaume|||0000-0002-9511-5999
author_role author
author2 Li, Shimin|||0000-0003-1695-0097
Llibre, Jaume|||0000-0002-9511-5999
author2_role author
author
dc.subject.none.fl_str_mv Gray-Scott model
Cubic polynomial system
Phase portraits
Bifurcation diagram
Hopf bifurcation
topic Gray-Scott model
Cubic polynomial system
Phase portraits
Bifurcation diagram
Hopf bifurcation
description We give a complete classification of the phase portraits in the Poincaré disk for the cubic polynomial systems ˙ x = 1-x-axy2, ˙ y = -by + axy2, in R2 according with the values of its two parameters a and b. These differential systems correspond to the Gray-Scott model. Moreover we provide the bifurcation diagram in the parameter plane (a,b) of these systems.
publishDate 2021
dc.date.none.fl_str_mv 2
2021-01-01
2021
2021-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AM
http://purl.org/coar/version/c_ab4af688f83e57aa
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/236644
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2020.124840
url https://ddd.uab.cat/record/236644
https://dx.doi.org/urn:doi:10.1016/j.jmaa.2020.124840
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 MTM2016-77278-P
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2017/SGR-1617
European Commission https://doi.org/10.13039/501100000780 777911
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
https://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
collection Dipòsit Digital de Documents de la UAB
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