Eigenvalue Decomposition as a Generalized Synchronization Cluster Analysis

Details Eigenvalue Decomposition as a Generalized Synchronization Cluster Analysis Eigenvalue Decomposition as a Generalized Synchronization Cluster Analysis

2007-06-22

arxiv.org/abs/0706.3375v3

International Journal of Bifurcation and Chaos, 17(10): 3493--3497, 2007

Physics

Data Analysis, Statistics and Probability

Submitted Oct 2005, accepted Jan 2006, "published" Oct 2007, actually available Jan 2008

Scientific paper

10.1142/S0218127407019251

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.

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