Basin stability approach for quantifying responses of multistable systems with parameters mismatch

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.

show abstract

“…Now, we show the additional information that can be obtained with extended basin stability method 18 . In Fig.…”

Section: Resultsmentioning

confidence: 99%

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

Brzeski

Wojewoda

Kapitaniak

et al. 2017

Sci Rep

Self Cite

View full text Add to dashboard Cite

show abstract

“…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].…”

Section: Introductionmentioning

confidence: 99%

Interval stability for complex systems

et al. 2018

View full text Add to dashboard Cite

Stability of dynamical systems against strong perturbations is an important problem of nonlinear dynamics relevant to many applications in various areas. Here, we develop a novel concept of interval stability, referring to the behavior of the perturbed system during a finite time interval. Based on this concept, we suggest new measures of stability, namely interval basin stability (IBS) and interval stability threshold (IST). IBS characterizes the likelihood that the perturbed system returns to the stable regime (attractor) in a given time. IST provides the minimal magnitude of the perturbation capable to disrupt the stable regime for a given interval of time. The suggested measures provide important information about the system susceptibility to external perturbations which may be useful for practical applications. Moreover, from a theoretical viewpoint the interval stability measures are shown to bridge the gap between linear and asymptotic stability. We also suggest numerical algorithms for quantification of the interval stability characteristics and demonstrate their potential for several dynamical systems of various nature, such as power grids and neural networks.

show abstract

“…Proposed idea has been successfully applied to asses the stability of power grids [63,85], systems with time delay [56], chimera states [79], stabilization of saddle fixed points in coupled oscillators [78] and brain dynamics [61]. In our previous papers we proposed extensions of this method [12]. Additionally to initial conditions we draw the parameters of the system.…”

Section: Introductionmentioning

confidence: 99%

Sample-Based Methods of Analysis for Multistable Dynamical Systems

Brzeski

Perlikowski

2018

Arch Computat Methods Eng

Self Cite

View full text Add to dashboard Cite

In this paper we present how sample based analysis can complement classical methods for analysis of dynamical systems. We describe how sample based algorithms can be utilized to obtain better understanding of complex dynamical phenomena, especially in multistable dynamical systems that are difficult for analytical investigations. Relying on the simple, direct numerical integration algorithms we are able to detect all possible solutions including hidden and rare attractors; investigate the ranges of stability in multiple parameters space; analyse the influence of parameters mismatch or model imperfections; assess the risk of dangerous or unwanted behaviour and reveal the structure of multidimensional phase space. For each mentioned application we present methodology, example on paradigmatic non-linear dynamical system and discuss practical applications. The presented methods of analysis can be applied to solve numerous of scientific problems originating from different disciplines. Moreover, their robustness and efficiency will grow with the upcoming increase of computational power.

show abstract

Basin stability approach for quantifying responses of multistable systems with parameters mismatch

Cited by 33 publications

References 30 publications

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

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

Interval stability for complex systems

Sample-Based Methods of Analysis for Multistable Dynamical Systems

Contact Info

Product

Resources

About