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

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 dy...

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Autores principales: Brzeski, P., Wojewoda, J., Kapitaniak, T., Kurths, J., Perlikowski, P.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5522450/
https://www.ncbi.nlm.nih.gov/pubmed/28733635
http://dx.doi.org/10.1038/s41598-017-05015-7
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author Brzeski, P.
Wojewoda, J.
Kapitaniak, T.
Kurths, J.
Perlikowski, P.
author_facet Brzeski, P.
Wojewoda, J.
Kapitaniak, T.
Kurths, J.
Perlikowski, P.
author_sort Brzeski, P.
collection PubMed
description 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.
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spelling pubmed-55224502017-07-26 Sample-based approach can outperform the classical dynamical analysis - experimental confirmation of the basin stability method Brzeski, P. Wojewoda, J. Kapitaniak, T. Kurths, J. Perlikowski, P. Sci Rep Article 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. Nature Publishing Group UK 2017-07-21 /pmc/articles/PMC5522450/ /pubmed/28733635 http://dx.doi.org/10.1038/s41598-017-05015-7 Text en © The Author(s) 2017 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
Brzeski, P.
Wojewoda, J.
Kapitaniak, T.
Kurths, J.
Perlikowski, P.
Sample-based approach can outperform the classical dynamical analysis - experimental confirmation of the basin stability method
title 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_short 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
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5522450/
https://www.ncbi.nlm.nih.gov/pubmed/28733635
http://dx.doi.org/10.1038/s41598-017-05015-7
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