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Title: Potentials and limits to basin stability estimation
Authors: Schultz, P.Menck, P.J.Heitzig, J.Kurths, J.
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Issue Date: 2017
Published in: New Journal of Physics Vol. 19 (2017), No. 2
Publisher: Bristol : Institute of Physics Publishing
Abstract: Stability assessment methods for dynamical systems have recently been complemented by basin stability and derived measures, i.e. probabilistic statements whether systems remain in a basin of attraction given a distribution of perturbations. Their application requires numerical estimation via Monte Carlo sampling and integration of differential equations. Here, we analyse the applicability of basin stability to systems with basin geometries that are challenging for this numerical method, having fractal basin boundaries and riddled or intermingled basins of attraction. We find that numerical basin stability estimation is still meaningful for fractal boundaries but reaches its limits for riddled basins with holes.
Keywords: attractor; basin stability; fractal basin boundaries; intermingled basins; riddled basins; Differential equations; Dynamical systems; Fractals; Monte Carlo methods; Numerical methods; Probability distributions; Stability; attractor; Basins of attraction; Fractal basin boundaries; intermingled basins; Monte Carlo sampling; Numerical estimation; Riddled basins; Stability assessment; System stability
DDC: 530
License: CC BY 3.0 Unported
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Appears in Collections:Physik

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