G. A. Okrokvertskhov

Correlation analysis of dynamical chaos

We study correlation and spectral properties of chaotic self-sustained oscillations of different types. It is shown that some classical models of stochastic processes can be used to describe behavior of autocorrelation functions of chaos. The influence of noise on chaotic systems is also considered.

Statistical properties of the instantaneous phase of noisy periodic and chaotic self-sustained oscillations

The statistics of the instantaneous phase of oscillations in dynamic systems with a noisy limit cycle is compared to the statistics of the instantaneous phase of oscillations in dynamic systems with a spiral chaotic attractor. Simulation of the phase dynamics of chaotic self-sustained oscillations by a Wiener process is considered. The results provided by various methods of determination of the instantaneous phase are analyzed.

CHAOTIC DYNAMICS OF A SPATIO-INHOMOGENEOUS MEDIUM

In the present paper we show that inhomogeneity of a continuous self-sustained oscillating medium can be a reason for the onset of chaotic behavior. It has been established that temporal chaotic dynamics typically arises in the medium with a linear mismatch of the natural frequency along a spatial coordinate, whereas a chaotic regime is not characteristic for the medium with randomly distributed frequencies. The interconnection has been revealed between the temporal chaotic behavior and the spatial formation of imperfect clusters. The spectral and correlation analysis as well as the linear analysis of stability of regular and chaotic regimes in the inhomogeneous medium are performed. The correlation of the instantaneous phase dynamics of oscillations with the behavior of autocorrelation functions has been examined. It has been established that the characteristics of temporal chaos correspond to a spiral attractor (Shilnikovs attractor).

Instantaneous phase dynamics and correlation analysis of spiral chaos. Experiments and a theoretical model

We show experimentally that the instantaneous phase dynamics has a great importance for the mixing in chaotic systems. In spite of some differences in the phase behavior, there is a common regularity of the correlations decay for a system in the regime of spiral chaos and a noisy self‐sustained quasiharmonic oscillator.

Theoretical and experimental analysis of regularities of autocorrelation function decay of the Lorentz attractor

In the present paper statistical properties of the Lorentz attractor are studied and general regularities of the temporal behavior of the autocorrelation function are determined. Using a symbolic dynamics the character of a random process of switchings between two symmetric areas of the attractor is investigated. It is shown that this process posseses the statistic of a telegraphic signal with a non Poisson distribution of impulses duration. It is demonstrated that the ACF of the Lorentz attractor decays with the linear law on small times. The theoretical and numerical results are compared with data of physical experimental data.