Potentials and limits to basin stability estimation
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 C...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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IOP Publishing
2017-01-01
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| Series: | New Journal of Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1088/1367-2630/aa5a7b |
| _version_ | 1797750878607769600 |
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| author | Paul Schultz Peter J Menck Jobst Heitzig Jürgen Kurths |
| author_facet | Paul Schultz Peter J Menck Jobst Heitzig Jürgen Kurths |
| author_sort | Paul Schultz |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-12T16:39:13Z |
| format | Article |
| id | doaj.art-27040668b528476fb9aa093ba269f3bb |
| institution | Directory Open Access Journal |
| issn | 1367-2630 |
| language | English |
| last_indexed | 2024-03-12T16:39:13Z |
| publishDate | 2017-01-01 |
| publisher | IOP Publishing |
| record_format | Article |
| series | New Journal of Physics |
| spelling | doaj.art-27040668b528476fb9aa093ba269f3bb2023-08-08T14:35:01ZengIOP PublishingNew Journal of Physics1367-26302017-01-0119202300510.1088/1367-2630/aa5a7bPotentials and limits to basin stability estimationPaul Schultz0https://orcid.org/0000-0002-1785-6476Peter J Menck1Jobst Heitzig2Jürgen Kurths3Potsdam Institute for Climate Impact Research, D-14412 Potsdam, Germany; Department of Physics, Humboldt University Berlin , D-12489 Berlin, GermanyPotsdam Institute for Climate Impact Research, D-14412 Potsdam, GermanyPotsdam Institute for Climate Impact Research, D-14412 Potsdam, GermanyPotsdam Institute for Climate Impact Research, D-14412 Potsdam, Germany; Department of Physics, Humboldt University Berlin , D-12489 Berlin, Germany; Institute for Complex Systems and Mathematical Biology, University of Aberdeen , AB24 3UE Aberdeen, United Kingdom; Department of Control Theory, Nizhny Novgorod State University , Gagarin Avenue 23, 606950 Nizhny Novgorod, RussiaStability 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.https://doi.org/10.1088/1367-2630/aa5a7battractorbasin stabilityfractal basin boundariesriddled basinsintermingled basins05.45.Df |
| spellingShingle | Paul Schultz Peter J Menck Jobst Heitzig Jürgen Kurths Potentials and limits to basin stability estimation New Journal of Physics attractor basin stability fractal basin boundaries riddled basins intermingled basins 05.45.Df |
| title | Potentials and limits to basin stability estimation |
| title_full | Potentials and limits to basin stability estimation |
| title_fullStr | Potentials and limits to basin stability estimation |
| title_full_unstemmed | Potentials and limits to basin stability estimation |
| title_short | Potentials and limits to basin stability estimation |
| title_sort | potentials and limits to basin stability estimation |
| topic | attractor basin stability fractal basin boundaries riddled basins intermingled basins 05.45.Df |
| url | https://doi.org/10.1088/1367-2630/aa5a7b |
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