Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems

Although planar quadratic differential systems and their applications have been studied in more than one thousand papers, we still have no complete understanding of these systems. In this paper we have two objectives. First we provide a brief bibliographical survey on the main results about quadrati...

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Detalles Bibliográficos
Autores: Li, Tao|||0000-0001-7376-4413, 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:257119
Acceso en línea:https://ddd.uab.cat/record/257119
https://dx.doi.org/urn:doi:10.1016/j.exmath.2021.01.003
Access Level:acceso abierto
Palabra clave:Separable system
Quadratic system
Phase portrait
Poincaré compactification
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spelling Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systemsLi, Tao|||0000-0001-7376-4413Llibre, Jaume|||0000-0002-9511-5999Separable systemQuadratic systemPhase portraitPoincaré compactificationAlthough planar quadratic differential systems and their applications have been studied in more than one thousand papers, we still have no complete understanding of these systems. In this paper we have two objectives. First we provide a brief bibliographical survey on the main results about quadratic systems. Here we do not consider the applications of these systems to many areas as in Physics, Chemist, Economics, Biology, … Second we characterize the new class of planar separable quadratic polynomial differential systems. For such class of systems we provide the normal forms which contain one parameter, and using the Poincaré compactification and the blow up technique, we prove that there exist 10 non-equivalent topological phase portraits in the Poincaré disc for the separable quadratic polynomial differential 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/257119https://dx.doi.org/urn:doi:10.1016/j.exmath.2021.01.003reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengAgencia 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, 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:2571192026-06-06T12:50:31Z
dc.title.none.fl_str_mv Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems
title Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems
spellingShingle Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems
Li, Tao|||0000-0001-7376-4413
Separable system
Quadratic system
Phase portrait
Poincaré compactification
title_short Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems
title_full Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems
title_fullStr Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems
title_full_unstemmed Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems
title_sort Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems
dc.creator.none.fl_str_mv Li, Tao|||0000-0001-7376-4413
Llibre, Jaume|||0000-0002-9511-5999
author Li, Tao|||0000-0001-7376-4413
author_facet Li, Tao|||0000-0001-7376-4413
Llibre, Jaume|||0000-0002-9511-5999
author_role author
author2 Llibre, Jaume|||0000-0002-9511-5999
author2_role author
dc.subject.none.fl_str_mv Separable system
Quadratic system
Phase portrait
Poincaré compactification
topic Separable system
Quadratic system
Phase portrait
Poincaré compactification
description Although planar quadratic differential systems and their applications have been studied in more than one thousand papers, we still have no complete understanding of these systems. In this paper we have two objectives. First we provide a brief bibliographical survey on the main results about quadratic systems. Here we do not consider the applications of these systems to many areas as in Physics, Chemist, Economics, Biology, … Second we characterize the new class of planar separable quadratic polynomial differential systems. For such class of systems we provide the normal forms which contain one parameter, and using the Poincaré compactification and the blow up technique, we prove that there exist 10 non-equivalent topological phase portraits in the Poincaré disc for the separable quadratic polynomial differential 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/257119
https://dx.doi.org/urn:doi:10.1016/j.exmath.2021.01.003
url https://ddd.uab.cat/record/257119
https://dx.doi.org/urn:doi:10.1016/j.exmath.2021.01.003
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 MTM2016-77278-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
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dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
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