Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces

In this paper, we study the dynamics of the FitzHugh-Nagumo system x˙=z,y˙=b(x-dy),z˙=x(x-1)(x-a)+y+cz having invariant algebraic surfaces. This system has four different types of invariant algebraic surfaces. The dynamics of the FitzHugh-Nagumo system having two of these classes of invariant algebr...

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Autores: Llibre, Jaume|||0000-0002-9511-5999, Tian, Yuzhou|||0000-0002-7624-4971
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:236667
Acceso en línea:https://ddd.uab.cat/record/236667
https://dx.doi.org/urn:doi:10.1007/s00033-020-01450-1
Access Level:acceso abierto
Palabra clave:Global dynamics
FitzHugh-Nagumo system
Invariant algebraic surface
Poincaré compactification
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spelling Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfacesLlibre, Jaume|||0000-0002-9511-5999Tian, Yuzhou|||0000-0002-7624-4971Global dynamicsFitzHugh-Nagumo systemInvariant algebraic surfacePoincaré compactificationIn this paper, we study the dynamics of the FitzHugh-Nagumo system x˙=z,y˙=b(x-dy),z˙=x(x-1)(x-a)+y+cz having invariant algebraic surfaces. This system has four different types of invariant algebraic surfaces. The dynamics of the FitzHugh-Nagumo system having two of these classes of invariant algebraic surfaces have been characterized in Valls (J Nonlinear Math Phys 26:569-578, 2019). Using the quasi-homogeneous directional blow-up and the Poincaré compactification, we describe the dynamics of the FitzHugh-Nagumo system having the two remaining classes of invariant algebraic surfaces. Moreover, for these FitzHugh-Nagumo systems we prove that they do not have limit cycles. 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/236667https://dx.doi.org/urn:doi:10.1007/s00033-020-01450-1reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengMinisterio 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 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:2366672026-06-06T12:50:31Z
dc.title.none.fl_str_mv Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces
title Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces
spellingShingle Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces
Llibre, Jaume|||0000-0002-9511-5999
Global dynamics
FitzHugh-Nagumo system
Invariant algebraic surface
Poincaré compactification
title_short Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces
title_full Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces
title_fullStr Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces
title_full_unstemmed Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces
title_sort Dynamics of the FitzHugh-Nagumo system having invariant algebraic surfaces
dc.creator.none.fl_str_mv Llibre, Jaume|||0000-0002-9511-5999
Tian, Yuzhou|||0000-0002-7624-4971
author Llibre, Jaume|||0000-0002-9511-5999
author_facet Llibre, Jaume|||0000-0002-9511-5999
Tian, Yuzhou|||0000-0002-7624-4971
author_role author
author2 Tian, Yuzhou|||0000-0002-7624-4971
author2_role author
dc.subject.none.fl_str_mv Global dynamics
FitzHugh-Nagumo system
Invariant algebraic surface
Poincaré compactification
topic Global dynamics
FitzHugh-Nagumo system
Invariant algebraic surface
Poincaré compactification
description In this paper, we study the dynamics of the FitzHugh-Nagumo system x˙=z,y˙=b(x-dy),z˙=x(x-1)(x-a)+y+cz having invariant algebraic surfaces. This system has four different types of invariant algebraic surfaces. The dynamics of the FitzHugh-Nagumo system having two of these classes of invariant algebraic surfaces have been characterized in Valls (J Nonlinear Math Phys 26:569-578, 2019). Using the quasi-homogeneous directional blow-up and the Poincaré compactification, we describe the dynamics of the FitzHugh-Nagumo system having the two remaining classes of invariant algebraic surfaces. Moreover, for these FitzHugh-Nagumo systems we prove that they do not have limit cycles.
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/236667
https://dx.doi.org/urn:doi:10.1007/s00033-020-01450-1
url https://ddd.uab.cat/record/236667
https://dx.doi.org/urn:doi:10.1007/s00033-020-01450-1
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv 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://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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