How to test for partially predictable chaos

Abstract For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation can split into an initial exponential decrease and a subsequent diffusive process on the chaotic attractor causing the final loss of predic...

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Autores principales:	Hendrik Wernecke, Bulcsú Sándor, Claudius Gros
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/b961888e2c554dbfbba85764bc8cd2b6
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id	oai:doaj.org-article:b961888e2c554dbfbba85764bc8cd2b6
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spelling	oai:doaj.org-article:b961888e2c554dbfbba85764bc8cd2b62021-12-02T15:06:13ZHow to test for partially predictable chaos10.1038/s41598-017-01083-x2045-2322https://doaj.org/article/b961888e2c554dbfbba85764bc8cd2b62017-04-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-01083-xhttps://doaj.org/toc/2045-2322Abstract For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation can split into an initial exponential decrease and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. Both processes can be either of the same or of very different time scales. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall extent of the attractor) for exceedingly long times and remain partially predictable. Standard tests for chaos widely use inter-orbital correlations as an indicator. However, testing partially predictable chaos yields mostly ambiguous results, as this type of chaos is characterized by attractors of fractally broadened braids. For a resolution we introduce a novel 0–1 indicator for chaos based on the cross-distance scaling of pairs of initially close trajectories. This test robustly discriminates chaos, including partially predictable chaos, from laminar flow. Additionally using the finite time cross-correlation of pairs of initially close trajectories, we are able to identify laminar flow as well as strong and partially predictable chaos in a 0–1 manner solely from the properties of pairs of trajectories.Hendrik WerneckeBulcsú SándorClaudius GrosNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-12 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Hendrik Wernecke Bulcsú Sándor Claudius Gros How to test for partially predictable chaos
description	Abstract For a chaotic system pairs of initially close-by trajectories become eventually fully uncorrelated on the attracting set. This process of decorrelation can split into an initial exponential decrease and a subsequent diffusive process on the chaotic attractor causing the final loss of predictability. Both processes can be either of the same or of very different time scales. In the latter case the two trajectories linger within a finite but small distance (with respect to the overall extent of the attractor) for exceedingly long times and remain partially predictable. Standard tests for chaos widely use inter-orbital correlations as an indicator. However, testing partially predictable chaos yields mostly ambiguous results, as this type of chaos is characterized by attractors of fractally broadened braids. For a resolution we introduce a novel 0–1 indicator for chaos based on the cross-distance scaling of pairs of initially close trajectories. This test robustly discriminates chaos, including partially predictable chaos, from laminar flow. Additionally using the finite time cross-correlation of pairs of initially close trajectories, we are able to identify laminar flow as well as strong and partially predictable chaos in a 0–1 manner solely from the properties of pairs of trajectories.
format	article
author	Hendrik Wernecke Bulcsú Sándor Claudius Gros
author_facet	Hendrik Wernecke Bulcsú Sándor Claudius Gros
author_sort	Hendrik Wernecke
title	How to test for partially predictable chaos
title_short	How to test for partially predictable chaos
title_full	How to test for partially predictable chaos
title_fullStr	How to test for partially predictable chaos
title_full_unstemmed	How to test for partially predictable chaos
title_sort	how to test for partially predictable chaos
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/b961888e2c554dbfbba85764bc8cd2b6
work_keys_str_mv	AT hendrikwernecke howtotestforpartiallypredictablechaos AT bulcsusandor howtotestforpartiallypredictablechaos AT claudiusgros howtotestforpartiallypredictablechaos
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How to test for partially predictable chaos

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