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 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.

Graphical Structure of Attraction Basins of Hidden Chaotic Attractors: The Rabinovich–Fabrikant System

“…The classification of attractors as being hidden or self-excited was introduced in connection with the discovery of the first hidden Chua attractor [Kuznetsov et al, 2010;Bragin et al, 2011;Leonov et al, 2012;Kiseleva et al, 2017;Stankevich et al, 2017] and has captured much attention of scientists from around the world (see, e.g. [Burkin & Khien, 2014;Li & Sprott, 2014;Pham et al, 2014;Chen et al, 2015;Kuznetsov et al, 2015;Saha et al, 2015;Semenov et al, 2015;Sharma et al, 2015;Zhusubaliyev et al, 2015;Wi et al, 2015;Jafari et al, 2016;Menacer et al, 2016;Ojoniyi & Njah, 2016;Pham et al, 2016;Rocha & Medrano, 2016;Wei et al, 2016;Zelinka, 2016;Borah & Roy, 2017;Brzeski et al, 2017;Feng & Pan, 2017;Jiang , 2016;Kuznetsov et al, 2017;Ma et al, 2017;Messias & Reinol, 2017;Singh & Roy, 2017;Volos et al, 2017;Wei et al, 2017;Zhang et al, 2017]).…”

Interval stability for complex systems

“…Recently, the concept of basin stability (BS) was suggested to describe the stability against large perturbations [15,[18][19][20]. The BS method was later used in various applications [21][22][23][24] and also confirmed experimentally [25]. BS is a probabilistic measure that characterizes the likelihood that the perturbation is 'safe', i.e.…”

Scenario of the Birth of Hidden Attractors in the Chua Circuit

“…The classification of attractors as being hidden or self-excited was introduced by G. Leonov and N. Kuznetsov in connection with the discovery of the first hidden Chua attractor [Leonov & Kuznetsov, 2009;Kuznetsov et al, 2010;Bragin et al, 2011;Leonov et al, 2012;Kuznetsov et al, 2013b;Leonov & Kuznetsov, 2013;Leonov et al, 2015a] and has captured attention of scientists from around the world (see, e.g. [Burkin & Khien, 2014;Li & Sprott, 2014;Chen, 2015;Saha et al, 2015;Feng & Pan, 2017;Zhusubaliyev et al, 2015;Danca, 2016;Kuznetsov et al, 2015;Chen et al, 2015a;Pham et al, 2014;Ojoniyi & Njah, 2016;Rocha & Medrano-T, 2016;Borah & Roy, 2017;Danca et al, 2017;Wei et al, 2016;Pham et al, 2016;Jafari et al, 2016;Dudkowski et al, 2016;Singh & Roy, 2017;Messias & Reinol, 2017;Brzeski et al, 2017;Wei et al, 2017;Chaudhuri & Prasad, 2014;Jiang et al, 2016;Volos et al, 2017]).…”