Potentials and limits to basin stability estimation. (2nd February 2017)

• Record Type: Journal Article
• Authors: Schultz, Paul; Menck, Peter J; Heitzig, Jobst; Kurths, Jürgen
• Is Part Of: New journal of physics. Volume 19:Number 2(2017:Feb.)
• Publication Date: 2017-02-02
• Subjects: attractor -- basin stability -- fractal basin boundaries -- riddled basins -- intermingled basins; 05.45.Df -- 05.45.Pq -- 05.10.-a -- 05.10.Ln -- 02.60.Jh; Physics -- Periodicals; Physics; Periodicals; 530.05
• DOI: 10.1088/1367-2630/aa5a7b
• Languages: English
• ISSNs: 1367-2630

Abstract

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.