Tipping phenomena in typical dynamical systems subjected to parameter drift

Abstract Tipping phenomena, i.e. dramatic changes in the possible long-term performance of deterministic systems subjected to parameter drift, are of current interest but have not yet been explored in cases with chaotic internal dynamics. Based on the example of a paradigmatic low-dimensional dissip...

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Autores principales:	Bálint Kaszás, Ulrike Feudel, Tamás Tél
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2019
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/f1fc5365ed4445339ef48b5f57984aad
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spelling	oai:doaj.org-article:f1fc5365ed4445339ef48b5f57984aad2021-12-02T15:09:47ZTipping phenomena in typical dynamical systems subjected to parameter drift10.1038/s41598-019-44863-32045-2322https://doaj.org/article/f1fc5365ed4445339ef48b5f57984aad2019-06-01T00:00:00Zhttps://doi.org/10.1038/s41598-019-44863-3https://doaj.org/toc/2045-2322Abstract Tipping phenomena, i.e. dramatic changes in the possible long-term performance of deterministic systems subjected to parameter drift, are of current interest but have not yet been explored in cases with chaotic internal dynamics. Based on the example of a paradigmatic low-dimensional dissipative system subjected to different scenarios of parameter drifts of non-negligible rates, we show that a number of novel types of tippings can be observed due to the topological complexity underlying general systems. Tippings from and into several coexisting attractors are possible, and one can find fractality-induced tipping, the consequence of the fractality of the scenario-dependent basins of attractions, as well as tipping into a chaotic attractor. Tipping from or through an extended chaotic attractor might lead to random tipping into coexisting regular attractors, and rate-induced tippings appear not abruptly as phase transitions, rather they show up gradually when the rate of the parameter drift is increased. Since chaotic systems of arbitrary time-dependence call for ensemble methods, we argue for a probabilistic approach and propose the use of tipping probabilities as a measure of tipping. We numerically determine these quantities and their parameter dependence for all tipping forms discussed.Bálint KaszásUlrike FeudelTamás TélNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 9, Iss 1, Pp 1-12 (2019)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Bálint Kaszás Ulrike Feudel Tamás Tél Tipping phenomena in typical dynamical systems subjected to parameter drift
description	Abstract Tipping phenomena, i.e. dramatic changes in the possible long-term performance of deterministic systems subjected to parameter drift, are of current interest but have not yet been explored in cases with chaotic internal dynamics. Based on the example of a paradigmatic low-dimensional dissipative system subjected to different scenarios of parameter drifts of non-negligible rates, we show that a number of novel types of tippings can be observed due to the topological complexity underlying general systems. Tippings from and into several coexisting attractors are possible, and one can find fractality-induced tipping, the consequence of the fractality of the scenario-dependent basins of attractions, as well as tipping into a chaotic attractor. Tipping from or through an extended chaotic attractor might lead to random tipping into coexisting regular attractors, and rate-induced tippings appear not abruptly as phase transitions, rather they show up gradually when the rate of the parameter drift is increased. Since chaotic systems of arbitrary time-dependence call for ensemble methods, we argue for a probabilistic approach and propose the use of tipping probabilities as a measure of tipping. We numerically determine these quantities and their parameter dependence for all tipping forms discussed.
format	article
author	Bálint Kaszás Ulrike Feudel Tamás Tél
author_facet	Bálint Kaszás Ulrike Feudel Tamás Tél
author_sort	Bálint Kaszás
title	Tipping phenomena in typical dynamical systems subjected to parameter drift
title_short	Tipping phenomena in typical dynamical systems subjected to parameter drift
title_full	Tipping phenomena in typical dynamical systems subjected to parameter drift
title_fullStr	Tipping phenomena in typical dynamical systems subjected to parameter drift
title_full_unstemmed	Tipping phenomena in typical dynamical systems subjected to parameter drift
title_sort	tipping phenomena in typical dynamical systems subjected to parameter drift
publisher	Nature Portfolio
publishDate	2019
url	https://doaj.org/article/f1fc5365ed4445339ef48b5f57984aad
work_keys_str_mv	AT balintkaszas tippingphenomenaintypicaldynamicalsystemssubjectedtoparameterdrift AT ulrikefeudel tippingphenomenaintypicaldynamicalsystemssubjectedtoparameterdrift AT tamastel tippingphenomenaintypicaldynamicalsystemssubjectedtoparameterdrift
_version_	1718387789595148288

Tipping phenomena in typical dynamical systems subjected to parameter drift

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