Vladimir Ponomarenko

The previously proposed method for quantifying the degree of synchronization between circulatory regulation loops is used to analyze the time realizations of healthy subjects. Statistical properties of the index are studied in the analysis of two-hour records of experimental signals. In the course of this work, we investigated the properties of the estimation of the degree of synchronization using temporal realizations with different length, and we investigated the features of synchronization between the control loops under study at a time equal to hundreds of characteristic periods.

We propose an original mathematical model for the human cardiovascular system. The model simulates the heart rate, autonomous control of heart, arterial pressure and cardiorespiratory interaction. Taking into account the self-excited autonomic control allowed us to reproduce the experimentally observed effects of phase synchronization between the control elements. The consistency of the proposed model is validated by quantitative and qualitative reproduction of spectral and statistical characteristics of real data from healthy subjects. Within physiological values of the parameters the model demonstrates chaotic dynamics and reproduces spontaneous interchange between the intervals of spontaneous and nonspontaneous behavior.

Reconstruction of equations of oscillatory systems from time series is an important problem, since results can be useful in different practical applications, including forecast of future dynamics, indirect measurement of parameters and diagnostics of coupling. The problem of reconstruction of coupling coefficients from time series of ensembles of a large number of oscillators is a practically valid problem. This study aims to develop a method of reconstruction of equations of an ensemble of identical neuron-like oscillators in the presence of time delays in couplings based on a given general form of equations.
The proposed method is based on the previously developed approach for reconstruction of diffusively coupled ensembles of time-delayed oscillators. To determine coupling coefficients, the target function is minimized with least-squares routine for each oscillator independently. This function characterizes the continuity of experimental data. Time delays are revealed using a special version of the gradient descent method adapted to the discrete case.
It is shown in the numerical experiment that the proposed method allows one to accurately estimate most of time delays (∼99%) even if short time series are used. The method is asymptotically unbiased.

A method is proposed for the reconstruction of first-order time-delay systems under external periodic driving from their time series. The method takes into account the structure of the model equation of the system, while constructing the autoregressive model. The proposed method allows one to reconstruct the delay time, the parameter characterizing the system inertial properties, the nonlinear function, and the amplitude and frequency of the external periodic driving. The method efficiency is demonstrated in a numerical experiment by reconstructing a number of different nonautonomous time-delay systems.