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Testing for Basins of Wada

Authors: Alvar Daza; Alexandre Wagemakers; Miguel A. F. Sanjuán; James A. Yorke;

Testing for Basins of Wada

Abstract

AbstractNonlinear 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.

Keywords

Fractal boundaries, Chaos, Wada, Article

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
45
Top 10%
Top 10%
Top 10%
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gold