Detecting phase synchronization in coupled oscillators by combining multivariate singular spectrum analysis and fast factorization of structured matrices

It is shown that a fast reliable block Fourier algorithm for the factorization of structured matrices improves computational efficiency of known method for detecting phase synchronization in a large system of coupled oscillators, based on multivariate singular spectrum analysis. In this paper, a novel algorithm for the detection of cluster synchronization in a system of coupled oscillators is proposed. The block Toeplitz covariance matrix of the total trajectory matrix is efficiently block-diagonalized by means of the Fast Fourier Transform by embedding it first into a block circulant matrix. The synchronization structure of the underlying multivariate data set is defined based on the 2D spatiotemporal eigenvalue spectrum. The benefits of the proposed method are illustrated by simulations of the phase synchronization effects in a chain of coupled chaotic Rossler oscillators and using multichannel electroencephalogram (EEG) recordings from epilepsy patients.