Colloquium: Basin Entropy: A new tool to explore uncertainty in dynamical systems

Date: April 21, 2017
Time: 3:00 pm – 4:15 pm

Location: Exploratory Hall L003 (Google map)

Featured Speaker:
Miguel Sanjuan
Universidad Rey Juan Carlos

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 log 2, the basin is fractal. This is joint work with Alvar Daza, Alexandre Wagemakers, Bertrand Georgeot and David Guéry-Odelin.

Refreshments will be served.