M. D. Prokhorov

Synchronization of low-frequency oscillations in the human cardiovascular system.

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.

Detecting synchronization of self-sustained oscillators by external driving with varying frequency

We propose a method for detecting the presence of a synchronization of a self-sustained oscillator by external driving with linearly varying frequency. The method is based on a continuous wavelet transform of the signals of the 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 a driven van der Pol oscillator and to experimental data of human heart rate variability and respiration.

Oscillation types, multistability, and basins of attractors in symmetrically coupled period-doubling systems

Abstract Symmetrically coupled nonlinear oscillator systems demonstrating transition to chaos via a sequence of period-doubling bifurcations under variation of the control parameter exhibit various types of mutual synchronization. For these coupled systems, with dissipatively coupled logistic maps, we consider a hierarchy of possible oscillation types using the value of the time shift between oscillations of the subsystems as a basis for the classification of multistable states. For oscillation states and their basins of attraction the ways of evolution are studied under variation of the parameters of nonlinearity and coupling. The obtained results are compared with those of physical experiment with a system of coupled, periodically driven nonlinear resonators.

Evaluation of 5‐Year Risk of Cardiovascular Events in Patients after Acute Myocardial Infarction Using Synchronization of 0.1‐Hz Rhythms in Cardiovascular System

Background: Synchronization between 0.1‐Hz rhythms in cardiovascular system is deteriorated at acute myocardial infarction (AMI) leading to a disruption of natural functional couplings within the system of autonomic regulation.

[Internal synchronization of the main 0.1-Hz rhythms in the autonomic control of the cardiovascular system].

Synchronization parameters of 0.1-Hz rhythms isolated from the heart rate and the oscillations of the blood volume in microcirculatory vessels were studied in 12 healthy subjects and 32 patients with acute myocardial infarction. Recordings of the electrocardiogram and the pulsogram from the distal phalanx of the index finger, as well as mechanical recording of respiration with the body in a horizontal position, were performed. In patients with myocardial infarction, the recordings were performed during the first three to five days and the third week after the infarction. Synchronization was tested by plotting phase differences and calculating the total percentage of phase synchronization. Synchronization parameters of 0.1-Hz rhythms were high in healthy subjects. In patients with acute myocardial infarction, synchronization of 0.1-Hz rhythms was considerably poorer. The data obtained suggest that the studied 0.1-Hz rhythms are two independent oscillatory processes that are synchronized in healthy subjects. However, this interaction may be disturbed in cardiovascular pathologies, e.g., myocardial infarction.

Phase and frequency locking of 0.1-Hz oscillations in heart rate and baroreflex control of blood pressure by breathing of linearly varying frequency as determined in healthy subjects

Functional interaction was studied between the subsystems that ensure autonomic control of the heart rate (HR) and blood pressure (BP) and give rise to 0.1-Hz oscillations in R-R intervals (RRI) and photoplethysmogram (PPG). Twenty-five recordings were obtained from 18- to 32-year-old healthy persons (six women and nineteen men). The RRI and PPG were recorded simultaneously while the respiration rate of a subject in the sitting position increased linearly from 0.05 Hz to 0.25 Hz within 25 min. Phase and frequency locking of 0.1-Hz oscillations by breathing proved to be possible in both RRI and PPG. The intervals of phase and frequency locking of oscillations by respiration differed in duration and relative position. These distinctions suggest that the mechanisms of autonomic 0.1-Hz control of HR and BP are functionally independent.

Hidden data transmission based on time-delayed feedback system with switched delay time

A scheme of hidden data transmission based on time-delayed feedback system with switched delay time is described. Efficiency of the proposed system and high resistance to interference in the communication channel is demonstrated in numerical experiments on model ring systems with time-delayed feedback.

Selection of optimal dose of beta-blocker treatment in myocardial infarction patients based on changes in synchronization between 0.1 Hz oscillations in heart rate and peripheral microcirculation.

Background Selection of the optimal dose of beta-blocker treatment in myocardial infarction (MI) patients is problematic because of a lack of well-established guidelines. Methods We evaluated changes in synchronization between 0.1 Hz oscillations in heart rate (HR) and plethysmographic peripheral microcirculation in response to a tilt-table test and to 3-month treatment with the highest tolerated beta-blocker (metoprolol) dose in 43 patients aged between 41 and 77 years with acute MI 6 months prior to the start of the study. Before the study the patients were treated with small doses of beta-blocker. Phase differences between HR and peripheral microcirculation oscillations were used to measure the degree of synchronization (S), and relative change in S from horizontal position was used to characterize the response to vertical tilt. Results Two groups of MI patients matched for clinical characteristics were identified on the basis of the results. The first group was composed of patients with decreased S as a response to vertical tilt at the beginning of the study. The patients with increased S during vertical tilt before treatment with the highest tolerated beta-blocker dose were attributed to the second group. The response to vertical tilt in the first group of patients was postulated to indicate the need to increase beta-blocker dose, and in turn, the response in the second group to indicate an already adequate beta-blocker dose. Conclusion Assessment of synchronization of 0.1 Hz HR and peripheral microcirculation oscillations as a response to a tilt test can possibly be used as a guideline for selecting beta-blocker dose in post-MI patients.

Recovery of parameters of delayed-feedback systems from chaotic time series

Methods for reconstructing a delay differential equation from the time series of an observable quantity are proposed for various classes of time-delay systems. The methods rely on knowledge of the distributions of extrema of the time series of observed oscillations and projection of the infinite-dimensional phase spaces of time-delay systems onto special low-dimensional subspaces. The effectiveness of the proposed methods is demonstrated by reconstructing delay differential equations from their chaotic solutions, including those corrupted by noise, and by constructing models of real time-delay systems from chaotic time series.

Intermittency of intermittencies.

A phenomenon of intermittency of intermittencies is discovered in the temporal behavior of two coupled complex systems. We observe for the first time the coexistence of two types of intermittent behavior taking place simultaneously near the boundary of the synchronization regime of coupled chaotic oscillators. This phenomenon is found both in the numerical and physiological experiments. The laws for both the distribution and mean length of laminar phases versus the control parameter values are analytically deduced. A very good agreement between the theoretical results and simulation is shown.