Phase Dynamics Based and Spectral Charateristics of Directional Couplings in Ensemble of Three Oscillators

The problem of directional coupling detection in ensembles of temporally evolving systems from observed time series is important in diverse fields. A small ensemble of three oscillators is a model of large ensembles which carry important features such as the distinction between direct and indirect influences and, therefore, allows the study of the methods for coupling detection in respect of their ability to distinguish between such influences and, hence, correctly identify directional couplings and provide their appropriate quantitative description. This work considers an ensemble of three exemplary oscillators as a test system to improve the coupling estimation method based on phase dynamics modeling and compare it to the spectral approach called Granger - Geweke spectrum. Possibilities of false conclusions about the structure of couplings are analyzed, sensitivity of both methods and interpretations of coupling characteristics are discussed.