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The aim of present research is refinement of the parameters and statistical properties of methods for diagnosing phase synchronization areas based on the dependence of the instantaneous phase difference of oscillations on time. Methods. Two methods are compared that allow one to identify of synchronization modes based on the dependence of the instantaneous phase difference of oscillations on time: a method based on an estimate of the phase coherence coefficient and a method based on a linear approximation of the instantaneous phase difference in a sliding window and an estimate of the slope of the approximating straight line. The phase synchronization of the low-frequency (0.04–0.15 Hz) components of the time series of interbeat intervals and blood pressure is analyzed. A mathematical model of the cardiovascular system is used to generate an ensemble of test data when analyzing the statistical properties of methods of phase synchronization analysis and refining their parameters. Test data is generated by modulating the coupling parameters between the autonomic control loops of blood circulation in the model, providing the known presence and absence of synchronization modes. Results. During the analysis of the model data, the values of the method parameters were refined. The sensitivity and specificity of the methods were evaluated. A higher sensitivity of the previously proposed method for detecting phase synchronization intervals in the analysis of non-stationary time series of the cardiovascular system is shown. Conclusion. In the analysis of non-stationary time series of the cardiovascular system shown the higher sensitivity of the method for detecting phase synchronization intervals, what based on a piecewise linear approximation of the instantaneous phase difference in a sliding window and an estimate of the slope of the approximating straight line.

Purpose of the work is to identify the directional coupling between the structures of the brain and the autonomic control of the heart rate variability, to analyze the changes in these coupling in sleep and in wakefulness. Infra-slow oscillations of the electroencephalograms potential and low-frequency components (0.04-0.15 Hz) of the interbeat intervals signal where analyzed using a sensitive method for identifying the directional coupling. The technique, based on modeling the dynamics of instantaneous phases of oscillations, made it possible to reveal the presence and quantify the directional couplings between the structures of the brain and the autonomic control of the heart rate variability. It was shown that the coupling coefficients in the frequency band of 0.04-0.15 Hz (associated mainly with sympathetic control of blood circulation), on average, decrease with falling asleep. We have also shown the asymmetry of coupling. At the same time, stronger connections were revealed in the direction from the autonomic control of the heart rate variability to the brain structures than in the opposite direction. It has been shown that the strength of such couplings decreases with increasing of sleep depth.