Planar Kolmogorov systems with infinitely many singular points at infinity

We classify the global dynamics of the five-parameter family of planar Kolmogorov systems y˙ = y (b0 + b1yz + b2y + b3z), z˙ = z (c0 + b1yz + b2y + b3z), which is obtained from the Lotka-Volterra systems of dimension three. These systems have infinitely many singular points at infinity. We give the...

Descripción completa

Detalles Bibliográficos
Autores: Diz-Pita, Érika|||0000-0002-7086-6614, Llibre, Jaume|||0000-0002-9511-5999, Otero-Espinar, M. Victoria|||0000-0002-0201-0523
Tipo de recurso: artículo
Fecha de publicación:2022
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:274780
Acceso en línea:https://ddd.uab.cat/record/274780
https://dx.doi.org/urn:doi:10.1142/S0218127422500651
Access Level:acceso abierto
Palabra clave:Kolmogorov system
Lotka-Volterra system
Phase portrait
Poincaré disc
id ES_37746c2d0161d37cf70e5d16716627e3
oai_identifier_str oai:ddd.uab.cat:274780
network_acronym_str ES
network_name_str España
repository_id_str
spelling Planar Kolmogorov systems with infinitely many singular points at infinityDiz-Pita, Érika|||0000-0002-7086-6614Llibre, Jaume|||0000-0002-9511-5999Otero-Espinar, M. Victoria|||0000-0002-0201-0523Kolmogorov systemLotka-Volterra systemPhase portraitPoincaré discWe classify the global dynamics of the five-parameter family of planar Kolmogorov systems y˙ = y (b0 + b1yz + b2y + b3z), z˙ = z (c0 + b1yz + b2y + b3z), which is obtained from the Lotka-Volterra systems of dimension three. These systems have infinitely many singular points at infinity. We give the topological classification of their phase portraits in the Poincaré disc, so we can describe the dynamics of these systems near infinity. We prove that these systems have 13 topologically distinct global phase portraits. 22022-01-0120222022-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/274780https://dx.doi.org/urn:doi:10.1142/S0218127422500651reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2020-115155GB-I00Ministerio de Educación, Cultura y Deporte https://doi.org/10.13039/501100003176 FPU17/02125Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2019-104658GB-I00Agència 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:2747802026-06-06T12:50:31Z
dc.title.none.fl_str_mv Planar Kolmogorov systems with infinitely many singular points at infinity
title Planar Kolmogorov systems with infinitely many singular points at infinity
spellingShingle Planar Kolmogorov systems with infinitely many singular points at infinity
Diz-Pita, Érika|||0000-0002-7086-6614
Kolmogorov system
Lotka-Volterra system
Phase portrait
Poincaré disc
title_short Planar Kolmogorov systems with infinitely many singular points at infinity
title_full Planar Kolmogorov systems with infinitely many singular points at infinity
title_fullStr Planar Kolmogorov systems with infinitely many singular points at infinity
title_full_unstemmed Planar Kolmogorov systems with infinitely many singular points at infinity
title_sort Planar Kolmogorov systems with infinitely many singular points at infinity
dc.creator.none.fl_str_mv Diz-Pita, Érika|||0000-0002-7086-6614
Llibre, Jaume|||0000-0002-9511-5999
Otero-Espinar, M. Victoria|||0000-0002-0201-0523
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, M. Victoria|||0000-0002-0201-0523
author_role author
author2 Llibre, Jaume|||0000-0002-9511-5999
Otero-Espinar, M. Victoria|||0000-0002-0201-0523
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 classify the global dynamics of the five-parameter family of planar Kolmogorov systems y˙ = y (b0 + b1yz + b2y + b3z), z˙ = z (c0 + b1yz + b2y + b3z), which is obtained from the Lotka-Volterra systems of dimension three. These systems have infinitely many singular points at infinity. We give the topological classification of their phase portraits in the Poincaré disc, so we can describe the dynamics of these systems near infinity. We prove that these systems have 13 topologically distinct global phase portraits.
publishDate 2022
dc.date.none.fl_str_mv 2
2022-01-01
2022
2022-01-01
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/274780
https://dx.doi.org/urn:doi:10.1142/S0218127422500651
url https://ddd.uab.cat/record/274780
https://dx.doi.org/urn:doi:10.1142/S0218127422500651
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 PID2020-115155GB-I00
Ministerio de Educación, Cultura y Deporte https://doi.org/10.13039/501100003176 FPU17/02125
Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 PID2019-104658GB-I00
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
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869406038478815232
score 15.300719

Similares en LA Referencia