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Basin entropy: a new tool to analyze uncertainty in dynamical systems

In nonlinear dynamics, basins of attraction link a given set of initial conditions to its corresponding final states. This notion appears in a broad range of applications where several outcomes are possible, which is a common situation in neuroscience, economy, astronomy, ecology and many other disc...

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Autores principales: Daza, Alvar, Wagemakers, Alexandre, Georgeot, Bertrand, Guéry-Odelin, David, Sanjuán, Miguel A. F.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group 2016
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4981859/
https://www.ncbi.nlm.nih.gov/pubmed/27514612
http://dx.doi.org/10.1038/srep31416
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author Daza, Alvar
Wagemakers, Alexandre
Georgeot, Bertrand
Guéry-Odelin, David
Sanjuán, Miguel A. F.
author_facet Daza, Alvar
Wagemakers, Alexandre
Georgeot, Bertrand
Guéry-Odelin, David
Sanjuán, Miguel A. F.
author_sort Daza, Alvar
collection PubMed
description In nonlinear dynamics, basins of attraction link a given set of initial conditions to its corresponding final states. This notion appears in a broad range of applications where several outcomes are possible, which is a common situation in neuroscience, economy, astronomy, ecology and many other disciplines. Depending on the nature of the basins, prediction can be difficult even in systems that evolve under deterministic rules. From this respect, a proper classification of this unpredictability is clearly required. To address this issue, we introduce the basin entropy, a measure to quantify this uncertainty. Its application is illustrated with several paradigmatic examples that allow us to identify the ingredients that hinder the prediction of the final state. The basin entropy provides an efficient method to probe the behavior of a system when different parameters are varied. Additionally, we provide a sufficient condition for the existence of fractal basin boundaries: when the basin entropy of the boundaries is larger than log2, the basin is fractal.
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spelling pubmed-49818592016-08-19 Basin entropy: a new tool to analyze uncertainty in dynamical systems Daza, Alvar Wagemakers, Alexandre Georgeot, Bertrand Guéry-Odelin, David Sanjuán, Miguel A. F. Sci Rep Article In nonlinear dynamics, basins of attraction link a given set of initial conditions to its corresponding final states. This notion appears in a broad range of applications where several outcomes are possible, which is a common situation in neuroscience, economy, astronomy, ecology and many other disciplines. Depending on the nature of the basins, prediction can be difficult even in systems that evolve under deterministic rules. From this respect, a proper classification of this unpredictability is clearly required. To address this issue, we introduce the basin entropy, a measure to quantify this uncertainty. Its application is illustrated with several paradigmatic examples that allow us to identify the ingredients that hinder the prediction of the final state. The basin entropy provides an efficient method to probe the behavior of a system when different parameters are varied. Additionally, we provide a sufficient condition for the existence of fractal basin boundaries: when the basin entropy of the boundaries is larger than log2, the basin is fractal. Nature Publishing Group 2016-08-12 /pmc/articles/PMC4981859/ /pubmed/27514612 http://dx.doi.org/10.1038/srep31416 Text en Copyright © 2016, The Author(s) http://creativecommons.org/licenses/by/4.0/ This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
spellingShingle Article
Daza, Alvar
Wagemakers, Alexandre
Georgeot, Bertrand
Guéry-Odelin, David
Sanjuán, Miguel A. F.
Basin entropy: a new tool to analyze uncertainty in dynamical systems
title Basin entropy: a new tool to analyze uncertainty in dynamical systems
title_full Basin entropy: a new tool to analyze uncertainty in dynamical systems
title_fullStr Basin entropy: a new tool to analyze uncertainty in dynamical systems
title_full_unstemmed Basin entropy: a new tool to analyze uncertainty in dynamical systems
title_short Basin entropy: a new tool to analyze uncertainty in dynamical systems
title_sort basin entropy: a new tool to analyze uncertainty in dynamical systems
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4981859/
https://www.ncbi.nlm.nih.gov/pubmed/27514612
http://dx.doi.org/10.1038/srep31416
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