Michael Rosenblum

Analysis of Bivariate Coupling by Means of Recurrence

In the analysis of coupled systems, various techniques have been developed to model and detect dependencies from observed bivariate time series. Most well-founded methods, like Granger-causality and partial coherence, are based on the theory of linear systems: on correlation functions, spectra and vector autoregressive processes. In this paper we discuss a nonlinear approach using recurrence.

DETECTION OF PHASE LOCKING FROM NOISY DATA: APPLICATION TO MAGNETOENCEPHALOGRAPHY

We use the concept of phase synchronization for the analysis of noisy nonstationary bivariate data. Phase synchronization is understood in a statistical sense as an existence of preferred values of the phase di erence, and two techniques are proposed for a reliable detection of synchronous epochs. These methods are applied to magnetoencephalograms and records of muscle activity of a Parkinsonian patient. We reveal that the temporal evolution of the peripheral tremor rhythms directly re ects the time course of the synchronization of abnormal activity between cortical motor areas.