Ascertaining when a basin is Wada: the merging method
Abstract Trying to imagine three regions separated by a unique boundary seems a difficult task. However, this is exactly what happens in many dynamical systems showing Wada basins. Here, we present a new perspective on the Wada property: A Wada boundary is the only one that remains unaltered under t...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2018-07-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-018-28119-0 |
| _version_ | 1818345848710365184 |
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| author | Alvar Daza Alexandre Wagemakers Miguel A. F. Sanjuán |
| author_facet | Alvar Daza Alexandre Wagemakers Miguel A. F. Sanjuán |
| author_sort | Alvar Daza |
| collection | DOAJ |
| description | Abstract Trying to imagine three regions separated by a unique boundary seems a difficult task. However, this is exactly what happens in many dynamical systems showing Wada basins. Here, we present a new perspective on the Wada property: A Wada boundary is the only one that remains unaltered under the action of merging the basins. This observation allows to develop a new method to test the Wada property, which is much faster than the previous ones. Furthermore, another major advantage of the merging method is that a detailed knowledge of the dynamical system is not required. |
| first_indexed | 2024-12-13T17:08:54Z |
| format | Article |
| id | doaj.art-6290cee4d357460d9b54ae4fbbeb9a74 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-12-13T17:08:54Z |
| publishDate | 2018-07-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-6290cee4d357460d9b54ae4fbbeb9a742022-12-21T23:37:37ZengNature PortfolioScientific Reports2045-23222018-07-01811810.1038/s41598-018-28119-0Ascertaining when a basin is Wada: the merging methodAlvar Daza0Alexandre Wagemakers1Miguel A. F. Sanjuán2Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan CarlosNonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan CarlosNonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan CarlosAbstract Trying to imagine three regions separated by a unique boundary seems a difficult task. However, this is exactly what happens in many dynamical systems showing Wada basins. Here, we present a new perspective on the Wada property: A Wada boundary is the only one that remains unaltered under the action of merging the basins. This observation allows to develop a new method to test the Wada property, which is much faster than the previous ones. Furthermore, another major advantage of the merging method is that a detailed knowledge of the dynamical system is not required.https://doi.org/10.1038/s41598-018-28119-0 |
| spellingShingle | Alvar Daza Alexandre Wagemakers Miguel A. F. Sanjuán Ascertaining when a basin is Wada: the merging method Scientific Reports |
| title | Ascertaining when a basin is Wada: the merging method |
| title_full | Ascertaining when a basin is Wada: the merging method |
| title_fullStr | Ascertaining when a basin is Wada: the merging method |
| title_full_unstemmed | Ascertaining when a basin is Wada: the merging method |
| title_short | Ascertaining when a basin is Wada: the merging method |
| title_sort | ascertaining when a basin is wada the merging method |
| url | https://doi.org/10.1038/s41598-018-28119-0 |
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