title: Basin entropy: a new tool to analyze uncertainty in dynamical systems.
abstract: 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.
authors: Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Móstoles, Madrid, Tulipán s/n, 28933, Spain.
authors: Alvar
authors: A
authors: Daza
authors: Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Móstoles, Madrid, Tulipán s/n, 28933, Spain.
authors: Alexandre
authors: A
authors: Wagemakers
authors: Laboratoire de Physique Théorique, IRSAMC, Université de Toulouse, CNRS, UPS, France.
authors: Bertrand
authors: B
authors: Georgeot
authors: Laboratoire Collisions, Agrégats, Réactivité, IRSAMC, Université de Toulouse, CNRS, UPS, France.
authors: David
authors: D
authors: Guéry-Odelin
authors: Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Móstoles, Madrid, Tulipán s/n, 28933, Spain.
authors: Miguel A F
authors: MA
authors: Sanjuán