On the zero-Hopf bifurcation of the Lotka-Volterra systems in R3

Here we study the Lotka-Volterra systems in R3, i.e. the differential systems of the form dxi/dt = xi(ri - Σ3j=1 aijxj), i = 1, 2, 3. It is known that some of these differential systems can have at least four periodic orbits bifurcating from one of their equilibrium points. Here we prove that there...

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Authors: Han, Maoan, Llibre, Jaume|||0000-0002-9511-5999, Tian, Yun
Format: article
Publication Date:2020
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:232162
Online Access:https://ddd.uab.cat/record/232162
https://dx.doi.org/urn:doi:10.3390/math8071137
Access Level:Open access
Keyword:Lotka-Volterra polynomial differential systems
Periodic orbit
Hopf bifurcation
Averaging theory
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spelling On the zero-Hopf bifurcation of the Lotka-Volterra systems in R3Han, MaoanLlibre, Jaume|||0000-0002-9511-5999Tian, YunLotka-Volterra polynomial differential systemsPeriodic orbitHopf bifurcationAveraging theoryHere we study the Lotka-Volterra systems in R3, i.e. the differential systems of the form dxi/dt = xi(ri - Σ3j=1 aijxj), i = 1, 2, 3. It is known that some of these differential systems can have at least four periodic orbits bifurcating from one of their equilibrium points. Here we prove that there are some of these differential systems exhibiting at least six periodic orbits bifurcating from one of their equilibrium points. The tool for proving this result is the averaging theory of third order. 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/232162https://dx.doi.org/urn:doi:10.3390/math8071137reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MDM-2014-0445Ministerio 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, 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:2321622026-06-06T12:50:31Z
dc.title.none.fl_str_mv On the zero-Hopf bifurcation of the Lotka-Volterra systems in R3
title On the zero-Hopf bifurcation of the Lotka-Volterra systems in R3
spellingShingle On the zero-Hopf bifurcation of the Lotka-Volterra systems in R3
Han, Maoan
Lotka-Volterra polynomial differential systems
Periodic orbit
Hopf bifurcation
Averaging theory
title_short On the zero-Hopf bifurcation of the Lotka-Volterra systems in R3
title_full On the zero-Hopf bifurcation of the Lotka-Volterra systems in R3
title_fullStr On the zero-Hopf bifurcation of the Lotka-Volterra systems in R3
title_full_unstemmed On the zero-Hopf bifurcation of the Lotka-Volterra systems in R3
title_sort On the zero-Hopf bifurcation of the Lotka-Volterra systems in R3
dc.creator.none.fl_str_mv Han, Maoan
Llibre, Jaume|||0000-0002-9511-5999
Tian, Yun
author Han, Maoan
author_facet Han, Maoan
Llibre, Jaume|||0000-0002-9511-5999
Tian, Yun
author_role author
author2 Llibre, Jaume|||0000-0002-9511-5999
Tian, Yun
author2_role author
author
dc.subject.none.fl_str_mv Lotka-Volterra polynomial differential systems
Periodic orbit
Hopf bifurcation
Averaging theory
topic Lotka-Volterra polynomial differential systems
Periodic orbit
Hopf bifurcation
Averaging theory
description Here we study the Lotka-Volterra systems in R3, i.e. the differential systems of the form dxi/dt = xi(ri - Σ3j=1 aijxj), i = 1, 2, 3. It is known that some of these differential systems can have at least four periodic orbits bifurcating from one of their equilibrium points. Here we prove that there are some of these differential systems exhibiting at least six periodic orbits bifurcating from one of their equilibrium points. The tool for proving this result is the averaging theory of third order.
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/232162
https://dx.doi.org/urn:doi:10.3390/math8071137
url https://ddd.uab.cat/record/232162
https://dx.doi.org/urn:doi:10.3390/math8071137
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 MDM-2014-0445
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/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
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