Testing for Basins of Wada

Nonlinear systems often give rise to fractal boundaries in phase space, hindering predictability. When a single boundary separates three or more different basins of attraction, we say that the set of basins has theWada property and initial conditions near that boundary are even more unpredictable. M...

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Bibliographic Details
Published in:Scientific reports 2015-11, Vol.5 (1), p.16579-16579, Article 16579
Main Authors: Daza, Alvar, Wagemakers, Alexandre, Sanjuán, Miguel A. F., Yorke, James A.
Format: Article
Language:English
Subjects:
639/705/1041
639/766/530/2803
Basins
Boundaries
Boxes
Dynamical systems
Fractals
Humanities and Social Sciences
multidisciplinary
Nonlinear systems
Science
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Summary:Nonlinear systems often give rise to fractal boundaries in phase space, hindering predictability. When a single boundary separates three or more different basins of attraction, we say that the set of basins has theWada property and initial conditions near that boundary are even more unpredictable. Many physical systems of interest with this topological property appear in the literature. However, so far the only approach to study Wada basins has been restricted to two-dimensional phase spaces. Here we report a simple algorithm whose purpose is to look for the Wada property in a given dynamical system. Another benefit of this procedure is the possibility to classify and study intermediate situations known as partially Wada boundaries.
ISSN:2045-2322
2045-2322
DOI:10.1038/srep16579