Eigenvalue Decomposition as a Generalized Synchronization Cluster Analysis
arXiv:0706.3375 · doi:10.1142/S0218127407019251
Abstract
Motivated by the recent demonstration of its use as a tool for the detection and characterization of phase-shape correlations in multivariate time series, we show that eigenvalue decomposition can also be applied to a matrix of indices of bivariate phase synchronization strength. The resulting method is able to identify clusters of synchronized oscillators, and to quantify their strength as well as the degree of involvement of an oscillator in a cluster. Since for the case of a single cluster the method gives similar results as our previous approach, it can be seen as a generalized Synchronization Cluster Analysis, extending its field of application to more complex situations. The performance of the method is tested by applying it to simulation data.
Submitted Oct 2005, accepted Jan 2006, "published" Oct 2007, actually available Jan 2008
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