Classifying basins of attraction using the basin entropy

A basin of attraction represents the set of initial conditions leading to a specific asymptotic state of a given dynamical system. Here, we provide a classification of the most common basins found in nonlinear dynamics with the help of the basin entropy. We have also found interesting connections be...

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Bibliographic Details
Published in:Chaos, solitons and fractals solitons and fractals, 2022-06, Vol.159, p.112112, Article 112112
Main Authors: Daza, Alvar, Wagemakers, Alexandre, Sanjuán, Miguel A.F.
Format: Article
Language:English
Subjects:
Basin entropy
Fractal basins
Fractal dimension
Lacunarity
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Summary:A basin of attraction represents the set of initial conditions leading to a specific asymptotic state of a given dynamical system. Here, we provide a classification of the most common basins found in nonlinear dynamics with the help of the basin entropy. We have also found interesting connections between the basin entropy and other measures used to characterize the unpredictability associated to the basins of attraction, such as the uncertainty exponent, the lacunarity or other different parameters related to the Wada property. •The basin entropy provides a natural framework to classify different types basins of attraction according to their unpredictability.•The most paradigmatic kind of basins (fractal, Wada, riddled, etc.) take extreme values in the parameter space of the basin entropy.•The basin entropy is compared with other typical measures associated to the unpredictability of the basins (uncertainty dimension, lacunarity, number of attractors), and the advantages of the basin entropy classification are discussed.
ISSN:0960-0779
1873-2887
DOI:10.1016/j.chaos.2022.112112