Search PubMed⌕ Search

Biomedical subjects

V S Anishchenko

Publications and source records attributed to V S Anishchenko.

10 recordsLinked to original sources
PubMed2002

Phase relationships between two or more interacting processes from one-dimensional time series. I. Basic theory.

A general approach is developed for the detection of phase relationships between two or more different oscillatory processes interacting within a single system, using one-dimensional time series only. It is based on the introduction of angles and radii of return times maps, and on studying the dynamics of the angles. An explicit unique relationship is derived between angles and the conventional phase difference introduced earlier for bivariate data. It is valid under conditions of weak forcing. This correspondence is confirmed numerically for a nonstationary process in a forced Van der Pol system. A model describing the angles' behavior for a dynamical system under weak quasiperiodic forcing with an arbitrary number of independent frequencies is derived.

Journal Article↗
PubMed2002

Phase relationships between two or more interacting processes from one-dimensional time series. II. Application to heart-rate-variability data.

The recently proposed approach to detect synchronization from univariate data is applied to heart-rate-variability (HRV) data from ten healthy humans. The approach involves introducing angles for return times map and studying their behavior. For filtered human HRV data, it is demonstrated that: (i) in many of the subjects studied, interactions between different processes within the cardiovascular system can be considered as weak, and the angles can be well described by the derived model; (ii) in some of the subjects the strengths of the interactions between the processes are sufficiently large that the angles map has a distinctive structure, which is not captured by our model; (iii) synchronization between the processes involved can often be detected; (iv) the instantaneous radii are rather disordered.

Journal Article↗
PubMed2001

Clustering of noise-induced oscillations.

The subject of our study is clustering in a population of excitable systems driven by Gaussian white noise and with randomly distributed coupling strength. The cluster state is frequency-locked state in which all functional units run at the same noise-induced frequency. Cooperative dynamics of this regime is described in terms of effective synchronization and noise-induced coherence.

Journal Article↗
PubMed2001

Effect of noise on the relaxation to an invariant probability measure of nonhyperbolic chaotic attractors.

We study the influence of external noise on the relaxation to an invariant probability measure for two types of nonhyperbolic chaotic attractors, a spiral (or coherent) and a noncoherent one. We find that for the coherent attractor the rate of mixing changes under the influence of noise, although the largest Lyapunov exponent remains almost unchanged. A mechanism of the noise influence on mixing is presented which is associated with the dynamics of the instantaneous phase of chaotic trajectories. This also explains why the noncoherent regime is robust against the presence of external noise.

Data Interpretation, Statistical↗
PubMed2001

Phase-frequency synchronization in a chain of periodic oscillators in the presence of noise and harmonic forcings.

We study numerically the effects of noise and periodic forcings on cluster synchronization in a chain of Van der Pol oscillators. We generalize the notion of effective synchronization to the case of a spatially extended system. It is shown that the structure of synchronized clusters can be effectively controlled by applying local external forcings. The effect of amplitude relations on the phase dynamics is also explored.

Journal Article↗
PubMed2001

Phase synchronization between several interacting processes from univariate data.

A novel approach is suggested for detecting the presence or absence of synchronization between two or three interacting processes with different time scales in univariate data. It is based on an angle-of-return-time map. A model is derived to describe analytically the behavior of angles for a periodic oscillator under weak periodic and quasiperiodic forcing. An explicit connection is demonstrated between the return angle and the phase of the external periodic forcing. The technique is tested on simulated nonstationary data and applied to human heart rate variability data.

Journal Article↗
PubMed2001

Chaotic dynamics from interspike intervals.

Considering two different mathematical models describing chaotic spiking phenomena, namely, an integrate-and-fire and a threshold-crossing model, we discuss the problem of extracting dynamics from interspike intervals (ISIs) and show that the possibilities of computing the largest Lyapunov exponent (LE) from point processes differ between the two models. We also consider the problem of estimating the second LE and the possibility to diagnose hyperchaotic behavior by processing spike trains. Since the second exponent is quite sensitive to the structure of the ISI series, we investigate the problem of its computation.

Journal Article↗
PubMed2001

Modelling the dynamics of angles of human R-R intervals.

Heart rate variability (HRV) data from young healthy humans is expanded into two components, namely, the angles and radii of a map of R-R intervals. It is shown that. for most subjects at rest breathing spontaneously, the map of successive angles reveals a highly deterministic structure after the frequency range below approximately 0.05 Hz has been filtered out. However, no obvious low-dimensional structure is found in the map of successive radii. A recently proposed model describing the map of angles for a periodic self-oscillator under external periodic and quasiperiodic forcing is successfully applied to model the dynamics of such angles.

Electrocardiography↗
PubMed2000

Extracting dynamics from threshold-crossing interspike intervals: possibilities and limitations.

In this paper we estimate dynamical characteristics of chaotic attractors from sequences of threshold-crossing interspike intervals, and study how the choice of the threshold level (which sets the equation of a secant plane) influences the results of the numerical computations. Under quite general conditions we show that the largest Lyapunov exponent can be estimated from a series of return times to the secant plane, even in the case when some of the loops of the phase space trajectory fail to cross this plane.

Algorithms↗