Phase portraits of a family of Kolmogorov systems depending on six parameters

We consider a general 3-dimensional Lotka-Volterra system with a rational first integral of degree two of the form H = xi yj zk. The restriction of this Lotka-Volterra system to each surface H(x, y, z) = h varying h ∈ R provide Kolmogorov systems. With the additional assumption that they have a Darb...

ver descrição completa

Detalhes bibliográficos
Autores: Diz-Pita, Érika|||0000-0002-7086-6614, Llibre, Jaume|||0000-0002-9511-5999, Otero Espinar, Maria Victoria
Formato: artículo
Fecha de publicación:2021
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:258885
Acesso em linha:https://ddd.uab.cat/record/258885
Access Level:acceso abierto
Palavra-chave:Kolmogorov system
Lotka-Volterra system
Phase portrait
Poincaré disc
id ES_812bb627b0a9a4daa406b99ef7a2e033
oai_identifier_str oai:ddd.uab.cat:258885
network_acronym_str ES
network_name_str España
repository_id_str
spelling Phase portraits of a family of Kolmogorov systems depending on six parametersDiz-Pita, Érika|||0000-0002-7086-6614Llibre, Jaume|||0000-0002-9511-5999Otero Espinar, Maria VictoriaKolmogorov systemLotka-Volterra systemPhase portraitPoincaré discWe consider a general 3-dimensional Lotka-Volterra system with a rational first integral of degree two of the form H = xi yj zk. The restriction of this Lotka-Volterra system to each surface H(x, y, z) = h varying h ∈ R provide Kolmogorov systems. With the additional assumption that they have a Darboux invariant of the form xl ym est they reduce to the Kolmogorov systems x˙ = x (a0 - µ(c1x + c2z2 + c3z)), z˙ = z (c0 + c1x + c2z2 + c3z)). We classify the phase portraits in the Poincaré disc of all these Kolmogorov systems which depend on six parameters. 22021-01-0120212021-01-01Articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/258885reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 MTM2016-79661-PMinisterio de Educación, Cultura y Deporte https://doi.org/10.13039/501100003176 FPU17/02125Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 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, la comunicació pública de l'obra i la creació d'obres derivades, fins i tot amb finalitats comercials, sempre i quan es reconegui l'autoria de l'obra original.https://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2588852026-06-06T12:50:31Z
dc.title.none.fl_str_mv Phase portraits of a family of Kolmogorov systems depending on six parameters
title Phase portraits of a family of Kolmogorov systems depending on six parameters
spellingShingle Phase portraits of a family of Kolmogorov systems depending on six parameters
Diz-Pita, Érika|||0000-0002-7086-6614
Kolmogorov system
Lotka-Volterra system
Phase portrait
Poincaré disc
title_short Phase portraits of a family of Kolmogorov systems depending on six parameters
title_full Phase portraits of a family of Kolmogorov systems depending on six parameters
title_fullStr Phase portraits of a family of Kolmogorov systems depending on six parameters
title_full_unstemmed Phase portraits of a family of Kolmogorov systems depending on six parameters
title_sort Phase portraits of a family of Kolmogorov systems depending on six parameters
dc.creator.none.fl_str_mv Diz-Pita, Érika|||0000-0002-7086-6614
Llibre, Jaume|||0000-0002-9511-5999
Otero Espinar, Maria Victoria
author Diz-Pita, Érika|||0000-0002-7086-6614
author_facet Diz-Pita, Érika|||0000-0002-7086-6614
Llibre, Jaume|||0000-0002-9511-5999
Otero Espinar, Maria Victoria
author_role author
author2 Llibre, Jaume|||0000-0002-9511-5999
Otero Espinar, Maria Victoria
author2_role author
author
dc.subject.none.fl_str_mv Kolmogorov system
Lotka-Volterra system
Phase portrait
Poincaré disc
topic Kolmogorov system
Lotka-Volterra system
Phase portrait
Poincaré disc
description We consider a general 3-dimensional Lotka-Volterra system with a rational first integral of degree two of the form H = xi yj zk. The restriction of this Lotka-Volterra system to each surface H(x, y, z) = h varying h ∈ R provide Kolmogorov systems. With the additional assumption that they have a Darboux invariant of the form xl ym est they reduce to the Kolmogorov systems x˙ = x (a0 - µ(c1x + c2z2 + c3z)), z˙ = z (c0 + c1x + c2z2 + c3z)). We classify the phase portraits in the Poincaré disc of all these Kolmogorov systems which depend on six parameters.
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
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/258885
url https://ddd.uab.cat/record/258885
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 MTM2016-79661-P
Ministerio de Educación, Cultura y Deporte https://doi.org/10.13039/501100003176 FPU17/02125
Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 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/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/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
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869411953808506880
score 15,301603

Registos relacionados