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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 principales: Corral, Álvaro, Sardanyés, Josep, Alsedà, Lluís
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6079039/
https://www.ncbi.nlm.nih.gov/pubmed/30082921
http://dx.doi.org/10.1038/s41598-018-30136-y
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author Corral, Álvaro
Sardanyés, Josep
Alsedà, Lluís
author_facet Corral, Álvaro
Sardanyés, Josep
Alsedà, Lluís
author_sort Corral, Álvaro
collection PubMed
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.
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spelling pubmed-60790392018-08-09 Finite-time scaling in local bifurcations Corral, Álvaro Sardanyés, Josep Alsedà, Lluís Sci Rep Article 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. Nature Publishing Group UK 2018-08-06 /pmc/articles/PMC6079039/ /pubmed/30082921 http://dx.doi.org/10.1038/s41598-018-30136-y Text en © The Author(s) 2018 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Corral, Álvaro
Sardanyés, Josep
Alsedà, Lluís
Finite-time scaling in local bifurcations
title 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_short Finite-time scaling in local bifurcations
title_sort finite-time scaling in local bifurcations
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6079039/
https://www.ncbi.nlm.nih.gov/pubmed/30082921
http://dx.doi.org/10.1038/s41598-018-30136-y
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