Eigenvalue Decomposition as a Generalized Synchronization Cluster Analysis

TL;DR

This paper introduces a generalized eigenvalue decomposition method for identifying and analyzing clusters of synchronized oscillators in multivariate time series, extending previous approaches to more complex scenarios.

Contribution

It presents a novel application of eigenvalue decomposition to synchronization indices, enabling detection and characterization of multiple oscillator clusters.

Findings

Effective in identifying synchronization clusters in simulated data

Quantifies cluster strength and oscillator involvement

Extends previous methods to complex synchronization patterns

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.