The reconstruction of the couplings structure in the ensemble of oscillators according to the time series via phase dynamics modeling

Topic. In this paper, we investigate the applicability of the known method for detecting the couplings between two oscillators, based on experimental phase dynamics modeling by phases time series in cases where there are several peaks in the signal power spectrum. The problem of revealing the structure of couplings in ensembles (presence, directions and intensity of interactions between elements) by experimental recordings of their oscillations is relevant for systems of different nature and applications. In its solution for the system of two oscillators, the method of reconstruction of phase dynamics models by time series has shown its efficiency provided that there is a single peak in the signal power spectrum. Aim. The investigation of the conditions for the applicability of this method in less favorable cases when there are several peaks in the power spectrum and the width of these peaks is significant. Methods. An ensemble of three Van der Pol oscillators is considered as a test system in the numerical experiment: two coupled oscillators were exposed to the simultaneous influence from the third one. Using the investigated method, the presence of a couplings between the oscillators was estimated from the time series of the oscillator phases. The numerical experiment was carried out at different values of oscillator parameters. Results. The possibility of false conclusions about the structure of couplings in such system is demonstrated. The diagnostic criterion of possible errors based on the estimation of the autocorrelation function of the phase dynamics model residues is proposed. To obtain reliable estimates of interactions in problem situations, pre-filtering of signals was tested.