WIAS Preprint No. 843, (2003)

Detection of mutual phase synchronization in multivariate signals and application to phase ensembles and chaotic data


  • Hutt, Axel
  • Daffertshofer, Andreas
  • Steinmetz, Ulrich

2010 Mathematics Subject Classification

  • 34C15 34C28 34D30

2008 Physics and Astronomy Classification Scheme

  • 02.50.Sk 05.45.Xt 05.10.-a


  • Multivariate analysis, transient behavior, phase synchronization, chaotic systems


The work presents a novel method for the detection of mutual phase synchronization in non-stationary time series. We show how the application of a cluster algorithm that considers spatio-temporal structures of data follows from the general condition of phase-synchronized data. In view of the topology of phasic data, we re-formulate the $K$-Means cluster algorithm on a flat torus and apply a segmentation index derived in an earlier work (Physica D 177,203-232(2003)). This index is extended by means of averaging in order to reflect phase synchronization in ensembles of multivariate time series. The method is illustrated using simulated multivariate phase dynamics and arrays of chaotic systems, in which temporal segments of phase-synchronized states are registered. A comparison with results from an existing bivariate synchronization index reveals major advantages of our method.

Appeared in

  • Physical Review E 68, 036219 (2003)

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