We investigate synchronization between the low-frequency oscillations of heart rate and blood pressure having in humans a basic frequency close to 0.1 Hz. A method is proposed for quantitative estimation of synchronization between these oscillating processes based on calculation of relative time of phase synchronization of oscillations. It is shown that healthy subjects exhibit on average substantially longer epochs of internal synchronization between the low-frequency oscillations in heart rate and blood pressure than patients after acute myocardial infarction.

For the cases of spontaneous respiration and paced respiration with a fixed frequency and linearly increasing frequency, we investigate synchronization between three main rhythmic processes governing the cardiovascular dynamics in humans, namely, the main heart rhythm, respiration, and the process whose fundamental frequency is close to 0.1 Hz. The analysis of the experimental records reveals synchronous regimes of different orders n:m between all the three main rhythms. The influence of the regime of breathing and the magnitude of heart rate variability on the degree of synchronization is considered.

We further develop the method proposed by Bezruchko et al. [Phys. Rev. E 64, 056216 (2001)] for the estimation of the parameters of time-delay systems from time series. Using this method we demonstrate a possibility of message extraction for a communication system with nonlinear mixing of information signal and chaotic signal of the time-delay system. The message extraction procedure is illustrated using both numerical and experimental data and different kinds of information signals.

We propose a method for detecting the presence of synchronization of self-sustained oscillator by external driving with linearly varying frequency. The method is based on a continuous wavelet transform of the signals of self-sustained oscillator and external force and allows one to distinguish the case of true synchronization from the case of spurious synchronization caused by linear mixing of the signals. We apply the method to driven van der Pol oscillator and to experimental data of human heart rate variability and respiration.