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 language | English |
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Article number | 023005 |
Pages (from-to) | 1-9 |
Number of pages | 8 |
Journal | New Journal of Physics |
Volume | 19 |
Early online date | 19 Jan 2017 |
DOIs | |
Publication status | Published - 2 Feb 2017 |
Bibliographical note
AcknowledgmentsThe authors gratefully acknowledge the support of BMBF, CoNDyNet, FK. 03SF0472A.
Keywords
- attractor
- basin stability
- fractal basin boundaries
- riddled basins
- intermingled basins