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.

Details

Title
Sample-based approach can outperform the classical dynamical analysis - experimental confirmation of the basin stability method
Author
Brzeski, P 1   VIAFID ORCID Logo  ; Wojewoda, J 2 ; Kapitaniak, T 2 ; Kurths, J 3 ; Perlikowski, P 2 

 Division of Dynamics, Lodz University of Technology, Lodz, Poland; Potsdam Institute for Climate Impact Research, Potsdam, Germany; Institute of Physics, Humboldt University of Berlin, Berlin, Germany 
 Division of Dynamics, Lodz University of Technology, Lodz, Poland 
 Potsdam Institute for Climate Impact Research, Potsdam, Germany; Institute of Physics, Humboldt University of Berlin, Berlin, Germany 
Pages
1-10
Publication year
2017
Publication date
Jul 2017
Publisher
Nature Publishing Group
e-ISSN
20452322
Source type
Scholarly Journal
Language of publication
English
ProQuest document ID
1956147750
Copyright
© 2017. This work is published under http://creativecommons.org/licenses/by/4.0/ (the “License”). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.