title: Phase dynamics of coupled oscillators reconstructed from data.
abstract: We systematically develop a technique for reconstructing the phase dynamics equations for coupled oscillators from data. For autonomous oscillators and for two interacting oscillators we demonstrate how phase estimates obtained from general scalar observables can be transformed to genuine phases. This allows us to obtain an invariant description of the phase dynamics in terms of the genuine, observable-independent phases. We discuss the importance of this transformation for characterization of strength and directionality of interaction from bivariate data. Moreover, we demonstrate that natural (autonomous) frequencies of oscillators can be recovered if several observations of coupled systems at different, yet unknown coupling strengths are available. We illustrate our method by several numerical examples and apply it to a human electrocardiogram and to a physical experiment with coupled metronomes.
authors.affiliation: Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht Strasse 24-25, D-14476 Potsdam, Germany.
authors.forename: Björn
authors.initials: B
authors.lastname: Kralemann
authors.forename: Laura
authors.initials: L
authors.lastname: Cimponeriu
authors.forename: Michael
authors.initials: M
authors.lastname: Rosenblum
authors.forename: Arkady
authors.initials: A
authors.lastname: Pikovsky
authors.forename: Ralf
authors.initials: R
authors.lastname: Mrowka