Potentials and Limits to Basin Stability Estimation

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

doi:10.1088/1367-2630/aa5a7b

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 language	English
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	https://doi.org/10.1088/1367-2630/aa5a7b
Publication status	Published - 2 Feb 2017

Bibliographical note

Acknowledgments
The authors gratefully acknowledge the support of BMBF, CoNDyNet, FK. 03SF0472A.

Keywords

attractor
basin stability
fractal basin boundaries
riddled basins
intermingled basins

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10.1088/1367-2630/aa5a7bLicence: CC BY

Potentials and limits to basin stability estimation
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Cite this

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AU - Schultz, Paul

AU - Menck, Peter J.

AU - Heitzig, Jobst

AU - Kurths, Jürgen

N1 - Acknowledgments The authors gratefully acknowledge the support of BMBF, CoNDyNet, FK. 03SF0472A.

PY - 2017/2/2

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N2 - 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.

AB - 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.

KW - attractor

KW - basin stability

KW - fractal basin boundaries

KW - riddled basins

KW - intermingled basins

U2 - 10.1088/1367-2630/aa5a7b

DO - 10.1088/1367-2630/aa5a7b

M3 - Article

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VL - 19

SP - 1

EP - 9

JO - New Journal of Physics

JF - New Journal of Physics

M1 - 023005

ER -

Potentials and Limits to Basin Stability Estimation

Abstract

Bibliographical note

Keywords

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