Examinando por Autor "Georgeot, Bertrand"

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    Ítem
    Basin entropy: a new tool to analyze uncertainty in dynamical systems
    (Nature, 2016-08-12) Daza, Alvar; Wagemakers, Alexandre; Georgeot, Bertrand; Guéry-Odelin, David; Sanjuán, Miguel A. F.
    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.
  • Miniatura
    Ítem
    Chaotic dynamics and fractal structures in experiments with cold atoms
    (APS, 2017-01-25) Daza, Alvar; Georgeot, Bertrand; Guéry-Odelin, David; Wagemakers, Alexandre; Sanjuán, Miguel A. F.
    We exploit tools from nonlinear dynamics to the detailed analysis of cold atom experiments. A powerful example is provided by the recent concept of basin entropy which allows to quantify the final state unpredictability that results from the complexity of the phase space geometry. We show here that this enables one to reliably infer the presence of fractal structures in phase space from direct measurements. We exemplify the method with numerical simulations in an experimental configuration made of two crossing laser guides and originally used as a matter wave splitter.