Finite-time scaling in local bifurcations

Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we have made use of the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete (deterministic) dynamical systems. We analytically derive...

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Autores: Corral, Álvaro|||0000-0002-5280-2692, Sardanyés, Josep|||0000-0001-7225-5158, Alsedà, Lluís|||0000-0001-9908-1063
Tipo de recurso: artículo
Fecha de publicación:2018
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:221286
Acceso en línea:https://ddd.uab.cat/record/221286
https://dx.doi.org/urn:doi:10.1038/s41598-018-30136-y
Access Level:acceso abierto
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spelling Finite-time scaling in local bifurcationsCorral, Álvaro|||0000-0002-5280-2692Sardanyés, Josep|||0000-0001-7225-5158Alsedà, Lluís|||0000-0001-9908-1063Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we have made use of the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete (deterministic) dynamical systems. We analytically derive finite-time scaling laws for two ubiquitous transitions given by the transcritical and the saddle-node bifurcation, obtaining exact expressions for the critical exponents and scaling functions. One of the scaling laws, corresponding to the distance of the dynamical variable to the attractor, turns out to be universal, in the sense that it holds for both bifurcations, yielding the same exponents and scaling function. Remarkably, the resulting scaling behavior in the transcritical bifurcation is precisely the same as the one in the (stochastic) Galton-Watson process. Our work establishes a new connection between thermodynamic phase transitions and bifurcations in low-dimensional dynamical systems, and opens new avenues to identify the nature of dynamical shifts in systems for which only short time series are available.Universitat Autònoma de Barcelona. Departament de Matemàtiques 22018-01-0120182018-01-01Articlehttp://purl.org/coar/resource_type/c_6501AMhttp://purl.org/coar/version/c_ab4af688f83e57aainfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/221286https://dx.doi.org/urn:doi:10.1038/s41598-018-30136-yreponame: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 Economía y Competitividad https://doi.org/10.13039/501100003329 FIS2015-71851-PMinisterio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2014-52209-C2-1-PAgencia Estatal de Investigación https://doi.org/10.13039/501100011033 MTM2017-86795-C3-1-PAgència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-1307Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 RYC-2017-22243open 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:2212862026-06-06T12:50:31Z
dc.title.none.fl_str_mv Finite-time scaling in local bifurcations
title Finite-time scaling in local bifurcations
spellingShingle Finite-time scaling in local bifurcations
Corral, Álvaro|||0000-0002-5280-2692
title_short Finite-time scaling in local bifurcations
title_full Finite-time scaling in local bifurcations
title_fullStr Finite-time scaling in local bifurcations
title_full_unstemmed Finite-time scaling in local bifurcations
title_sort Finite-time scaling in local bifurcations
dc.creator.none.fl_str_mv Corral, Álvaro|||0000-0002-5280-2692
Sardanyés, Josep|||0000-0001-7225-5158
Alsedà, Lluís|||0000-0001-9908-1063
author Corral, Álvaro|||0000-0002-5280-2692
author_facet Corral, Álvaro|||0000-0002-5280-2692
Sardanyés, Josep|||0000-0001-7225-5158
Alsedà, Lluís|||0000-0001-9908-1063
author_role author
author2 Sardanyés, Josep|||0000-0001-7225-5158
Alsedà, Lluís|||0000-0001-9908-1063
author2_role author
author
dc.contributor.none.fl_str_mv Universitat Autònoma de Barcelona. Departament de Matemàtiques
description Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we have made use of the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete (deterministic) dynamical systems. We analytically derive finite-time scaling laws for two ubiquitous transitions given by the transcritical and the saddle-node bifurcation, obtaining exact expressions for the critical exponents and scaling functions. One of the scaling laws, corresponding to the distance of the dynamical variable to the attractor, turns out to be universal, in the sense that it holds for both bifurcations, yielding the same exponents and scaling function. Remarkably, the resulting scaling behavior in the transcritical bifurcation is precisely the same as the one in the (stochastic) Galton-Watson process. Our work establishes a new connection between thermodynamic phase transitions and bifurcations in low-dimensional dynamical systems, and opens new avenues to identify the nature of dynamical shifts in systems for which only short time series are available.
publishDate 2018
dc.date.none.fl_str_mv 2
2018-01-01
2018
2018-01-01
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/221286
https://dx.doi.org/urn:doi:10.1038/s41598-018-30136-y
url https://ddd.uab.cat/record/221286
https://dx.doi.org/urn:doi:10.1038/s41598-018-30136-y
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 Economía y Competitividad https://doi.org/10.13039/501100003329 FIS2015-71851-P
Ministerio de Economía y Competitividad https://doi.org/10.13039/501100003329 MTM2014-52209-C2-1-P
Agencia Estatal de Investigación https://doi.org/10.13039/501100011033 MTM2017-86795-C3-1-P
Agència de Gestió d'Ajuts Universitaris i de Recerca https://doi.org/10.13039/501100003030 2014/SGR-1307
Ministerio de Ciencia e Innovación https://doi.org/10.13039/501100004837 RYC-2017-22243
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
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repository.mail.fl_str_mv
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