Global dynamics of a Lotka-Volterra system in R³

In this work we consider the Lotka-Volterra system in R³ x˙ = -x(x - y - z), y˙ = -y(-x + y - z), z˙ = -z(-x - y + z), introduced recently in [7], and studied also in [8] and [14]. In the first two papers the authors mainly studied the integrability of this differential system, while in the third pa...

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Autores: Llibre, Jaume|||0000-0002-9511-5999, Martínez, Y. Paulina|||0000-0003-1430-6636, Valls, Clàudia|||0000-0001-8279-1229
Formato: artículo
Fecha de publicación:2020
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:228109
Acesso em linha:https://ddd.uab.cat/record/228109
https://dx.doi.org/urn:doi:10.1080/14029251.2020.1757240
Access Level:acceso abierto
Palavra-chave:Lotka-Volterra system
Phase portraits
Poincaré ball
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spelling Global dynamics of a Lotka-Volterra system in R³Llibre, Jaume|||0000-0002-9511-5999Martínez, Y. Paulina|||0000-0003-1430-6636Valls, Clàudia|||0000-0001-8279-1229Lotka-Volterra systemPhase portraitsPoincaré ballIn this work we consider the Lotka-Volterra system in R³ x˙ = -x(x - y - z), y˙ = -y(-x + y - z), z˙ = -z(-x - y + z), introduced recently in [7], and studied also in [8] and [14]. In the first two papers the authors mainly studied the integrability of this differential system, while in the third paper they studied the system as a Hamilton-Poisson system, and also started the analysis of its dynamics. Here we provide the global phase portraits of this 3-dimensional Lotka-Volterra system in the Poincaré ball, that is in R³ adding its extension to the infinity. 22020-01-0120202020-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/228109https://dx.doi.org/urn:doi:10.1080/14029251.2020.1757240reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2016-77278-PMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MDM-2014-0445Agència 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 material està protegit per drets d'autor i/o drets afins. Podeu utilitzar aquest material en funció del que permet la legislació de drets d'autor i drets afins d'aplicació al vostre cas. Per a d'altres usos heu d'obtenir permís del(s) titular(s) de drets.https://rightsstatements.org/vocab/InC/1.0/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:2281092026-06-06T12:50:31Z
dc.title.none.fl_str_mv Global dynamics of a Lotka-Volterra system in R³
title Global dynamics of a Lotka-Volterra system in R³
spellingShingle Global dynamics of a Lotka-Volterra system in R³
Llibre, Jaume|||0000-0002-9511-5999
Lotka-Volterra system
Phase portraits
Poincaré ball
title_short Global dynamics of a Lotka-Volterra system in R³
title_full Global dynamics of a Lotka-Volterra system in R³
title_fullStr Global dynamics of a Lotka-Volterra system in R³
title_full_unstemmed Global dynamics of a Lotka-Volterra system in R³
title_sort Global dynamics of a Lotka-Volterra system in R³
dc.creator.none.fl_str_mv Llibre, Jaume|||0000-0002-9511-5999
Martínez, Y. Paulina|||0000-0003-1430-6636
Valls, Clàudia|||0000-0001-8279-1229
author Llibre, Jaume|||0000-0002-9511-5999
author_facet Llibre, Jaume|||0000-0002-9511-5999
Martínez, Y. Paulina|||0000-0003-1430-6636
Valls, Clàudia|||0000-0001-8279-1229
author_role author
author2 Martínez, Y. Paulina|||0000-0003-1430-6636
Valls, Clàudia|||0000-0001-8279-1229
author2_role author
author
dc.subject.none.fl_str_mv Lotka-Volterra system
Phase portraits
Poincaré ball
topic Lotka-Volterra system
Phase portraits
Poincaré ball
description In this work we consider the Lotka-Volterra system in R³ x˙ = -x(x - y - z), y˙ = -y(-x + y - z), z˙ = -z(-x - y + z), introduced recently in [7], and studied also in [8] and [14]. In the first two papers the authors mainly studied the integrability of this differential system, while in the third paper they studied the system as a Hamilton-Poisson system, and also started the analysis of its dynamics. Here we provide the global phase portraits of this 3-dimensional Lotka-Volterra system in the Poincaré ball, that is in R³ adding its extension to the infinity.
publishDate 2020
dc.date.none.fl_str_mv 2
2020-01-01
2020
2020-01-01
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/228109
https://dx.doi.org/urn:doi:10.1080/14029251.2020.1757240
url https://ddd.uab.cat/record/228109
https://dx.doi.org/urn:doi:10.1080/14029251.2020.1757240
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2016-77278-P
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MDM-2014-0445
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://rightsstatements.org/vocab/InC/1.0/
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://rightsstatements.org/vocab/InC/1.0/
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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