Potentials and Limits to Basin Stability Estimation

Paul Schultz, Peter J. Menck, Jobst Heitzig, Jürgen Kurths

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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. This requires numerical estimation via Monte-Carlo sampling and integration of differential equations. Here, we analyze the applicability of basin stability to systems with basin geometries 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.
Original languageEnglish
Article number023005
Pages (from-to)1-9
Number of pages8
JournalNew Journal of Physics
Volume19
Early online date19 Jan 2017
DOIs
Publication statusPublished - 2 Feb 2017

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Keywords

  • attractor
  • basin stability
  • fractal basin boundaries
  • riddled basins
  • intermingled basins

Cite this

Schultz, P., Menck, P. J., Heitzig, J., & Kurths, J. (2017). Potentials and Limits to Basin Stability Estimation. New Journal of Physics, 19, 1-9. [023005]. https://doi.org/10.1088/1367-2630/aa5a7b