The purpose of this work was to identify couplings between three interacting biological oscillators using phase dynamics modeling and to determine the influence of a pathological condition on the configuration of unidirectional triplewise couplings in these systems.

Methods. To identify these couplings, we used phase dynamics modeling for weakly coupled systems. Estimates of the connectivity matrix of the three-oscillator network were used to characterize the interconnections between the systems.

Results. We verified the accuracy of identifying couplings for a model of three chaotic R¨ossler oscillators with known directional couplings. We also identified the possibility of additional influence of one oscillator on another, or the combined influence of two oscillators on a third, with increasing coupling strength. For experimental time series corresponding to respiratory rate fluctuations, blood pressure variability curves, and variability of neuronal activity intervals in the medulla oblongata, we identified the influence of a pathological condition on the emergence of additional couplings in triple interactions between oscillators in the nervous, respiratory, and cardiovascular systems.

Conclusion. The application of phase dynamics modeling to assess the characteristics of the coupling between three interacting biological oscillators demonstrated the importance of physiological state in assessing the predominant influence of one oscillator over another.