Sample-based approach can outperform the classical dynamical analysis - experimental confirmation of the basin stability method

Abstract In this paper we show the first broad experimental confirmation of the basin stability approach. The basin stability is one of the sample-based approach methods for analysis of the complex, multidimensional dynamical systems. We show that investigated method is a reliable tool for the analy...

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Autores principales:	P. Brzeski, J. Wojewoda, T. Kapitaniak, J. Kurths, P. Perlikowski
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2017
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/b517193b2c8046f58429474a1cd145ab
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spelling	oai:doaj.org-article:b517193b2c8046f58429474a1cd145ab2021-12-02T16:08:23ZSample-based approach can outperform the classical dynamical analysis - experimental confirmation of the basin stability method10.1038/s41598-017-05015-72045-2322https://doaj.org/article/b517193b2c8046f58429474a1cd145ab2017-07-01T00:00:00Zhttps://doi.org/10.1038/s41598-017-05015-7https://doaj.org/toc/2045-2322Abstract In this paper we show the first broad experimental confirmation of the basin stability approach. The basin stability is one of the sample-based approach methods for analysis of the complex, multidimensional dynamical systems. We show that investigated method is a reliable tool for the analysis of dynamical systems and we prove that it has a significant advantages which make it appropriate for many applications in which classical analysis methods are difficult to apply. We study theoretically and experimentally the dynamics of a forced double pendulum. We examine the ranges of stability for nine different solutions of the system in a two parameter space, namely the amplitude and the frequency of excitation. We apply the path-following and the extended basin stability methods (Brzeski et al., Meccanica 51(11), 2016) and we verify obtained theoretical results in experimental investigations. Comparison of the presented results show that the sample-based approach offers comparable precision to the classical method of analysis. However, it is much simpler to apply and can be used despite the type of dynamical system and its dimensions. Moreover, the sample-based approach has some unique advantages and can be applied without the precise knowledge of parameter values.P. BrzeskiJ. WojewodaT. KapitaniakJ. KurthsP. PerlikowskiNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 7, Iss 1, Pp 1-10 (2017)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q P. Brzeski J. Wojewoda T. Kapitaniak J. Kurths P. Perlikowski Sample-based approach can outperform the classical dynamical analysis - experimental confirmation of the basin stability method
description	Abstract In this paper we show the first broad experimental confirmation of the basin stability approach. The basin stability is one of the sample-based approach methods for analysis of the complex, multidimensional dynamical systems. We show that investigated method is a reliable tool for the analysis of dynamical systems and we prove that it has a significant advantages which make it appropriate for many applications in which classical analysis methods are difficult to apply. We study theoretically and experimentally the dynamics of a forced double pendulum. We examine the ranges of stability for nine different solutions of the system in a two parameter space, namely the amplitude and the frequency of excitation. We apply the path-following and the extended basin stability methods (Brzeski et al., Meccanica 51(11), 2016) and we verify obtained theoretical results in experimental investigations. Comparison of the presented results show that the sample-based approach offers comparable precision to the classical method of analysis. However, it is much simpler to apply and can be used despite the type of dynamical system and its dimensions. Moreover, the sample-based approach has some unique advantages and can be applied without the precise knowledge of parameter values.
format	article
author	P. Brzeski J. Wojewoda T. Kapitaniak J. Kurths P. Perlikowski
author_facet	P. Brzeski J. Wojewoda T. Kapitaniak J. Kurths P. Perlikowski
author_sort	P. Brzeski
title	Sample-based approach can outperform the classical dynamical analysis - experimental confirmation of the basin stability method
title_short	Sample-based approach can outperform the classical dynamical analysis - experimental confirmation of the basin stability method
title_full	Sample-based approach can outperform the classical dynamical analysis - experimental confirmation of the basin stability method
title_fullStr	Sample-based approach can outperform the classical dynamical analysis - experimental confirmation of the basin stability method
title_full_unstemmed	Sample-based approach can outperform the classical dynamical analysis - experimental confirmation of the basin stability method
title_sort	sample-based approach can outperform the classical dynamical analysis - experimental confirmation of the basin stability method
publisher	Nature Portfolio
publishDate	2017
url	https://doaj.org/article/b517193b2c8046f58429474a1cd145ab
work_keys_str_mv	AT pbrzeski samplebasedapproachcanoutperformtheclassicaldynamicalanalysisexperimentalconfirmationofthebasinstabilitymethod AT jwojewoda samplebasedapproachcanoutperformtheclassicaldynamicalanalysisexperimentalconfirmationofthebasinstabilitymethod AT tkapitaniak samplebasedapproachcanoutperformtheclassicaldynamicalanalysisexperimentalconfirmationofthebasinstabilitymethod AT jkurths samplebasedapproachcanoutperformtheclassicaldynamicalanalysisexperimentalconfirmationofthebasinstabilitymethod AT pperlikowski samplebasedapproachcanoutperformtheclassicaldynamicalanalysisexperimentalconfirmationofthebasinstabilitymethod
_version_	1718384553639280640

Sample-based approach can outperform the classical dynamical analysis - experimental confirmation of the basin stability method

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