Defining universality classes for three different local bifurcations

Detalhes bibliográficos
Autor(a) principal: Leonel, Edson D. [UNESP]
Data de Publicação: 2016
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1016/j.cnsns.2016.04.008
http://hdl.handle.net/11449/168586
Resumo: The convergence to the fixed point at a bifurcation and near it is characterized via scaling formalism for three different types of local bifurcations of fixed points in differential equations, namely: (i) saddle-node; (ii) transcritical; and (iii) supercritical pitchfork. At the bifurcation, the convergence is described by a homogeneous function with three critical exponents α, β and z. A scaling law is derived hence relating the three exponents. Near the bifurcation the evolution towards the fixed point is given by an exponential function whose relaxation time is marked by a power law of the distance of the bifurcation point with an exponent δ. The four exponents α, β, z and δ can be used to defined classes of universality for the local bifurcations of fixed points in differential equations.
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spelling Defining universality classes for three different local bifurcationsCritical exponentsLocal bifurcationsScaling lawThe convergence to the fixed point at a bifurcation and near it is characterized via scaling formalism for three different types of local bifurcations of fixed points in differential equations, namely: (i) saddle-node; (ii) transcritical; and (iii) supercritical pitchfork. At the bifurcation, the convergence is described by a homogeneous function with three critical exponents α, β and z. A scaling law is derived hence relating the three exponents. Near the bifurcation the evolution towards the fixed point is given by an exponential function whose relaxation time is marked by a power law of the distance of the bifurcation point with an exponent δ. The four exponents α, β, z and δ can be used to defined classes of universality for the local bifurcations of fixed points in differential equations.Departamento de Física UNESP - Universidade Estadual Paulista, Av. 24A, 1515 Bela VistaAbdus Salam International Center for Theoretical Physics, Strada Costiera 11Departamento de Física UNESP - Universidade Estadual Paulista, Av. 24A, 1515 Bela VistaUniversidade Estadual Paulista (Unesp)Abdus Salam International Center for Theoretical PhysicsLeonel, Edson D. [UNESP]2018-12-11T16:42:03Z2018-12-11T16:42:03Z2016-10-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article520-528application/pdfhttp://dx.doi.org/10.1016/j.cnsns.2016.04.008Communications in Nonlinear Science and Numerical Simulation, v. 39, p. 520-528.1007-5704http://hdl.handle.net/11449/16858610.1016/j.cnsns.2016.04.0082-s2.0-849639560142-s2.0-84963956014.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengCommunications in Nonlinear Science and Numerical Simulation1,372info:eu-repo/semantics/openAccess2024-01-17T06:29:58Zoai:repositorio.unesp.br:11449/168586Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T23:18:35.742305Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv Defining universality classes for three different local bifurcations
title Defining universality classes for three different local bifurcations
spellingShingle Defining universality classes for three different local bifurcations
Leonel, Edson D. [UNESP]
Critical exponents
Local bifurcations
Scaling law
title_short Defining universality classes for three different local bifurcations
title_full Defining universality classes for three different local bifurcations
title_fullStr Defining universality classes for three different local bifurcations
title_full_unstemmed Defining universality classes for three different local bifurcations
title_sort Defining universality classes for three different local bifurcations
author Leonel, Edson D. [UNESP]
author_facet Leonel, Edson D. [UNESP]
author_role author
dc.contributor.none.fl_str_mv Universidade Estadual Paulista (Unesp)
Abdus Salam International Center for Theoretical Physics
dc.contributor.author.fl_str_mv Leonel, Edson D. [UNESP]
dc.subject.por.fl_str_mv Critical exponents
Local bifurcations
Scaling law
topic Critical exponents
Local bifurcations
Scaling law
description The convergence to the fixed point at a bifurcation and near it is characterized via scaling formalism for three different types of local bifurcations of fixed points in differential equations, namely: (i) saddle-node; (ii) transcritical; and (iii) supercritical pitchfork. At the bifurcation, the convergence is described by a homogeneous function with three critical exponents α, β and z. A scaling law is derived hence relating the three exponents. Near the bifurcation the evolution towards the fixed point is given by an exponential function whose relaxation time is marked by a power law of the distance of the bifurcation point with an exponent δ. The four exponents α, β, z and δ can be used to defined classes of universality for the local bifurcations of fixed points in differential equations.
publishDate 2016
dc.date.none.fl_str_mv 2016-10-01
2018-12-11T16:42:03Z
2018-12-11T16:42:03Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1016/j.cnsns.2016.04.008
Communications in Nonlinear Science and Numerical Simulation, v. 39, p. 520-528.
1007-5704
http://hdl.handle.net/11449/168586
10.1016/j.cnsns.2016.04.008
2-s2.0-84963956014
2-s2.0-84963956014.pdf
url http://dx.doi.org/10.1016/j.cnsns.2016.04.008
http://hdl.handle.net/11449/168586
identifier_str_mv Communications in Nonlinear Science and Numerical Simulation, v. 39, p. 520-528.
1007-5704
10.1016/j.cnsns.2016.04.008
2-s2.0-84963956014
2-s2.0-84963956014.pdf
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv Communications in Nonlinear Science and Numerical Simulation
1,372
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 520-528
application/pdf
dc.source.none.fl_str_mv Scopus
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
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