Biomedical subjects
Publications and source records attributed to A G Balanov.
We show that characteristic features of noise-induced spatiotemporal patterns in excitable media can be effectively controlled by applying delayed feedback. Actually, by variation of the time delay and of the strength of the feedback one can deliberately change both spatial and temporal coherence, as well as adjust the characteristic time scales.
The influence of time-delayed feedback upon the spatiotemporal current density patterns is investigated in a model of a semiconductor nanostructure, namely a double-barrier resonant tunneling diode. The parameters are chosen below the Hopf bifurcation, where the only stable state of the system is a spatially inhomogeneous "filamentary" steady state. The addition of weak Gaussian white noise to the system gives rise to spatially inhomogeneous self-sustained temporal oscillations that can be quite coherent. We show that applying a time-delayed feedback can either increase or decrease the regularity of the noise-induced dynamics in this spatially extended system. Using linear stability analysis, we can explain these effects, depending on the length of the delay interval. Furthermore, we study the influence of this additional control term upon the deterministic behavior of the system, which can change significantly depending on the choice of parameters.
We show that in the mutual synchronization of periodic oscillators, besides an attracting torus, there is also a saddle torus that plays an equally important role. We demonstrate that the saddle and stable tori form an elegant structure, allowing for a variety of phenomena, both known and new, related to the origin and evolution of coexisting synchronous regimes (phase multistability).
We study the effect of time delayed feedback control in the form proposed by Pyragas on deterministic chaos in the Rössler system. We reveal the general bifurcation diagram in the parameter plane of time delay tau and feedback strength K which allows one to explain the phenomena that have been discovered in some previous works. We show that the bifurcation diagram has essentially a multileaf structure that constitutes multistability: the larger the tau, the larger the number of attractors that can coexist in the phase space. Feedback induces a large variety of regimes nonexistent in the original system, among them tori and chaotic attractors born from them. Finally, we estimate how the parameters of delayed feedback influence the periods of limit cycles in the system.
We investigate the influence of noise upon the dynamics of the current density distribution in a model of a semiconductor nanostructure, namely, a double barrier resonant tunneling diode. We fix the parameters of the device below the Hopf bifurcation, where the only stable state of the system is a spatially inhomogeneous "filamentary" steady state. We show that the addition of weak Gaussian white noise to the system gives rise to spatially inhomogeneous oscillations that can be quite coherent. As the noise intensity grows, the oscillations tend to become more and more spatially homogeneous, while simultaneously the temporal correlation of the oscillations decreases. Thus, while on one hand noise destroys temporal coherence, on the other hand it enhances the spatial coherence of the current density pattern.
Time-delayed feedback is exploited for controlling noise-induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in an excitable system, delayed feedback can stabilize the frequency of oscillations against variation of noise strength. Also, for fixed noise intensity, the phenomenon of entrainment of the basic oscillation period by the delayed feedback occurs. This allows one to steer the time scales of noise-induced motion by changing the time delay.
Cardiorespiratory synchronization under paced respiration is studied systematically as the respiration frequency is changed between 3 and 30 breaths per min. We plot a one-dimensional cut of the classical picture of synchronization regions along the line defining the current breathing amplitude. The existence of n:m synchronization regions of finite width is demonstrated for each of six subjects studied. The statistics of the different types of synchronization and their stability are discussed.
A fundamental relationship between coherence resonance (CR) and phase synchronization in a self-sustained system in the presence of noise is addressed. A Van der Pol system synchronized by external forcing is taken as an example. It is shown that, in breaking down synchronization, applied noise creates a new ordered motion whose coherence depends resonantly on its intensity, i.e., CR occurs. The same is true for both types of synchronization, via phase locking and via suppression: only the mechanisms of CR differ. The result is valid for any order n:m of synchronization.
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.
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.
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.
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.
Lag synchronization denotes a particular form of synchronization in which the amplitudes of two interacting, nonidentical chaotic oscillators are correlated but there is a characteristic time delay between them. We study transitions to and between different forms of synchronization for the attractors defined as "in-phase" and "out-of-phase" and investigate the processes by which lag synchronization is lost in two coupled Rössler systems. With a small frequency mismatch between the two systems, these processes are related to the occurrence of a peculiar form of basin structure as more and more periodic orbits embedded into the synchronized chaotic state become unstable in a transverse direction.