Reconstruction of parameters and unobserved variables of a semiconductor laser with optical feedback from intensity time series.

We propose a method for the reconstruction of time-delayed feedback systems having unobserved variables from scalar time series. The method is based on the modified initial condition approach, which allows one to significantly reduce the number of starting guesses for an unobserved variable with a time delay. The proposed method is applied to the reconstruction of the Lang-Kobayashi equations, which describe the dynamics of a single-mode semiconductor laser with external optical feedback. We consider the case where only the time series of laser intensity is observable and the other two variables of the model are hidden. The dependence of the quality of the system reconstruction on the accuracy of assignment of starting guesses for unobserved variables and unknown laser parameters is studied. The method could be used for testing the security of information transmission in laser-based chaotic communication systems.

Autonomic control is a source of dynamical chaos in the cardiovascular system.

The origin of complex irregular dynamics in a cardiovascular system is still being actively debated. Some hypotheses suggest the crucial role of stochastic modulation of cardiovascular parameters, while others argue for the importance of cardiac pacemakers' chaotic deterministic dynamics. In the present study, we estimate the largest Lyapunov exponent and the correlation dimension for the 4-h experimental interbeat intervals and the chaotic signals generated by the mathematical model of the cardiovascular system. We study the complexity of the mathematical model for such cases as the autonomic blockade, the exclusion of all the stochastic components, and the absence of variability of respiration. The obtained results suggest that the complexity of the heart rate variability is largely due to the chaotic dynamics in the loops of autonomic control of circulation.

Model of Human Cardiovascular System Containing a Loop for the Autonomic Control of Mean Arterial Pressure.

We proposed a model of human cardiovascular system that describes the cardiac cycle, the autonomic regulation of heart and vessels, the baroreflex, and the formation of arterial pressure. The model also makes allowance for the influence of respiration on these processes. It was found that an allowance for nonlinearity and insertion of a loop for the autonomic control of mean arterial pressure (having the form of self oscillating time-delay system) enables to obtain model signals with statistical and spectral characteristics that are qualitatively and quantitatively similar to.those for experimental signals. The model reproduces the phenomenon of synchronization of the loop for mean arterial pressure regulation with a basic frequency of approximately 10 s by the signal of respiration.

Reconstruction of ensembles of coupled time-delay systems from time series.

We propose a method to recover from time series the parameters of coupled time-delay systems and the architecture of couplings between them. The method is based on a reconstruction of model delay-differential equations and estimation of statistical significance of couplings. It can be applied to networks composed of nonidentical nodes with an arbitrary number of unidirectional and bidirectional couplings. We test our method on chaotic and periodic time series produced by model equations of ensembles of diffusively coupled time-delay systems in the presence of noise, and apply it to experimental time series obtained from electronic oscillators with delayed feedback coupled by resistors.

[Phase and frequency locking of 0.1 Hz oscillations in heart rhythm and baroreflex control of arterial pressure by respiration with linearly varying frequency in healthy subjects].

We studied the features of functional interaction between the subsystems of autonomic control of heart rate (HR) and arterial pressure (AP) giving rise to 0.1 Hz oscillations in R-R intervals (RRI) and photoplethysmogram (PPG). The study included 25 healthy subjects (6 women and 19 men) aged between 18 and 32 years. The signals of RRI, PPG and respiration were simultaneously recorded under breathing with a frequency linearly increasing from 0.05 Hz to 0.25 Hz within 25 minutes in a sitting position of a subject. The possibility of phase and frequency locking of 0.1 Hz oscillations in RRI and PPG by respiration is shown. We revealed that theses oscillations have different width and location of the intervals of phase and frequency locking by respiration. This distinction points to the functional independence between the mechanisms of autonomic control of 0.1 Hz oscillations in RRI and PPG.

[Investigation of biophysical features of interaction between 0.1 Hz oscillations in heart rate variability and distal blood flow variability].

We studied biophysical features of interaction between 0.1 Hz oscillations in heart rate variability (HRV) and distal blood flow (DBF) variability in healthy subjects and patients after acute myocardial infarction (MI). 125 patients after acute MI (72 male and 53 female) aged between 30 and 83 years and 33 healthy subjects (23 male and 10 female) aged between 20 and 46 years were included in the study. The duration of prospective study of MI patients was one year. We estimated the delay in coupling between 0.1 Hz oscillations in H RV and DBF variability. It is found out that in healthy subjects the delay in coupling from heart rate to DBF is less than delay in coupling from DBF to heart rate. Acute MI results mainly in disruption of coupling from heart rate to DBF. This coupling is partially restored in one year after acute MI, but the delay in coupling remains significantly smaller than in healthy subjects. The features of coupling from DBF to heart rate are restored in MI patients within three weeks after infarction. After this period the delay in this coupling in MI patients is approximately the same as it is in healthy subjects.

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.

Estimation of coupling between oscillators from short time series via phase dynamics modeling: limitations and application to EEG data.

We demonstrate in numerical experiments that estimators of strength and directionality of coupling between oscillators based on modeling of their phase dynamics [D. A. Smirnov and B. P. Bezruchko, Phys. Rev. E 68, 046209 (2003)] are widely applicable. Namely, although the expressions for the estimators and their confidence bands are derived for linear uncoupled oscillators under the influence of independent sources of Gaussian white noise, they turn out to allow reliable characterization of coupling from relatively short time series for different properties of noise, significant phase nonlinearity of the oscillators, and nonvanishing coupling between them. We apply the estimators to analyze a two-channel human intracranial epileptic electroencephalogram (EEG) recording with the purpose of epileptic focus localization.

EEG nonstationarity during intracranially recorded seizures: statistical and dynamical analysis.

OBJECTIVE: The investigation of nonstationarity in complex, multivariable signals, such as electroencephalographic (EEG) recordings, requires the application of different and novel approaches to analysis. In this study, we have divided the EEG recordings during epileptic seizures into sequential stages using spectral and statistical analysis, and have as well reconstructed discrete-time models (maps) that reflect dynamical (deterministic) properties of the EEG voltage time series. METHODS: Intracranial human EEG recordings with epileptic seizures from three different subjects with medically intractable temporal lobe epilepsy were studied. The methods of statistical (power spectra, wavelet spectra, and one-dimensional probability distribution functions) and dynamical (comparison of dynamical models) nonstationarity analysis were applied. RESULTS: Dynamical nonstationarity analysis revealed more detailed inner structure within the seizures than the statistical analysis. Three or four stages with different dynamics are typically present within seizures. The difference between interictal activity and seizure events was also more evident through dynamical analysis. CONCLUSIONS: Nonstationarity analysis can reveal temporal structure within an epileptic seizure, which could further understanding of how seizures evolve. The method could also be used for identification of seizure onset. SIGNIFICANCE: Our approach reveals new information about the temporal structure of seizures, which is inaccessible using conventional methods.

Reconstruction of time-delay systems from chaotic time series.

We propose a method that allows one to estimate the parameters of model scalar time-delay differential equations from time series. The method is based on a statistical analysis of time intervals between extrema in the time series. We verify our method by using it for the reconstruction of time-delay differential equations from their chaotic solutions and for modeling experimental systems with delay-induced dynamics from their chaotic time series.

Role of transient processes for reconstruction of model equations from time series.

We perform a global reconstruction of differential and difference equations, which model an object in a wide domain of a phase space, from a time series. The efficiency of using time realizations of transient processes for this purpose is demonstrated. Time series of transients are shown to have some advantages for the realization of a procedure of model structure optimization.

Constructing nonautonomous differential equations from experimental time series.

An approach to constructing model differential equations of harmonically driven systems is proposed. It is a modification of the standard global reconstruction technique: an algebraic polynomial which coefficients depend on time is used for approximation. Efficiency and details of the approach are demonstrated by various numerical and natural examples.