Georgia Institute of Technology College of Sciences

A new approach based on Wasserstein distances, which are numerical costs ofan optimal transportation problem, allows to analyze nonlinear phenomena ina robust manner. The long-term behavior is reconstructed from time series, resulting in aprobability distribution over phase space. Each pair of probabilitydistributions is then assigned a numerical distance that quantifies thedifferences in their dynamical properties. From the totality of all these distances a low-dimensional representation ina Euclidean spaceis derived. This representation shows the functional relationships betweenthe dynamical systems under study. It allows to assess synchronizationproperties and also offers a new way of numerical bifurcation analysis.