title: Partial phase synchronization for multivariate synchronizing systems.
abstract: Graphical models applying partial coherence to multivariate time series are a powerful tool to distinguish direct and indirect interdependencies in multivariate linear systems. We carry over the concept of graphical models and partialization analysis to phase signals of nonlinear synchronizing systems. This procedure leads to the partial phase synchronization index which generalizes a bivariate phase synchronization index to the multivariate case and reveals the coupling structure in multivariate synchronizing systems by differentiating direct and indirect interactions. This ensures that no false positive conclusions are drawn concerning the interaction structure in multivariate synchronizing systems. By application to the paradigmatic model of a coupled chaotic Roessler system, the power of the partial phase synchronization index is demonstrated.
authors.affiliation: FDM, Freiburg Center for Data Analysis and Modeling, University of Freiburg, Eckerstrasse 1, 79104 Freiburg, Germany. schelter@fdm.uni-freiburg.de
authors.forename: Björn
authors.initials: B
authors.lastname: Schelter
authors.forename: Matthias
authors.initials: M
authors.lastname: Winterhalder
authors.forename: Rainer
authors.initials: R
authors.lastname: Dahlhaus
authors.forename: Jürgen
authors.initials: J
authors.lastname: Kurths
authors.forename: Jens
authors.initials: J
authors.lastname: Timmer