Basin entropy: a new tool to analyze uncertainty in dynamical systems

In nonlinear dynamics, basins of attraction link a given set of initial conditions to its corresponding final states. This notion appears in a broad range of applications where several outcomes are possible, which is a common situation in neuroscience, economy, astronomy, ecology and many other disc...

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Bibliographic Details
Published in:Scientific reports 2016-08, Vol.6 (1), p.31416-31416, Article 31416
Main Authors: Daza, Alvar, Wagemakers, Alexandre, Georgeot, Bertrand, Guéry-Odelin, David, Sanjuán, Miguel A. F.
Format: Article
Language:English
Subjects:
639/705/1041
639/766/530
Astronomy
Basins
Boundaries
Classification
Entropy
Humanities and Social Sciences
multidisciplinary
Nervous system
Nonlinear Sciences
Nonlinear systems
Science
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Summary:In nonlinear dynamics, basins of attraction link a given set of initial conditions to its corresponding final states. This notion appears in a broad range of applications where several outcomes are possible, which is a common situation in neuroscience, economy, astronomy, ecology and many other disciplines. Depending on the nature of the basins, prediction can be difficult even in systems that evolve under deterministic rules. From this respect, a proper classification of this unpredictability is clearly required. To address this issue, we introduce the basin entropy, a measure to quantify this uncertainty. Its application is illustrated with several paradigmatic examples that allow us to identify the ingredients that hinder the prediction of the final state. The basin entropy provides an efficient method to probe the behavior of a system when different parameters are varied. Additionally, we provide a sufficient condition for the existence of fractal basin boundaries: when the basin entropy of the boundaries is larger than log2, the basin is fractal.
ISSN:2045-2322
2045-2322
DOI:10.1038/srep31416