ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


Обзоры актуальных проблем нелинейной динамики

Phenomenon of the van der pol equation

  This review is devoted to the famous Dutch scientist Balthasar van der Pol, who made a significant contribution to the development of radio­engineering, physics and mathematics. The review outlines only one essential point of his work, associated with the equation that bears his  name, and has a surprisingly wide range of applications in natural sciences. In this review we discuss the following matters. • The biography of van der Pol, history of his equation and supposed precursors. • The contribution of A.A. Andronov in the theory of self­oscillations.

Progress and prospect of wavelet transform application to the analysis of nonstationary nonlinear dates in contemporary geophysics

The presented paper is an analytical review of the methods and examples of applications of the continuous and discrete wavelet transform in geophysical study. The possibility of the extension of application of the wavelet­based methods in geophysics is also considered.

Stochastic bifurcations

The modern knowledges of bifurcations of dynamical systems in the presence of noise are presenred. The main definitions are given and certain typical examples of the bifurcations in the presence of additive and multiplicative noise are considered.

Vacuum particle creation in strong fields: statistical aspects

In the present review we summarize the known informations about the evolution of a strongly nonequilibrium quasiparticle electron­positron plasma created from the vacuum under the influence of a strong nonstationary electromagnetic field. The methodical basis is given by quantum kinetic equations of the non­Markovian type which are nonperturbative consequences of the basic equations of QED in the collisionless approximation.

Longitudinal coherence of optical field

Spatial coherence of an optical field in a direction of its propagation depending on parameters of frequency and angular spectra of the field is considered. The expressions for function and length of longitudinal coherence are derived depending on width of frequency and angular spectra. The competing influence of angular and frequency spectra of a field on its longitudinal coherence is discussed. The experimental study with use the Michelson interferometer of longitudinal shift confirming theoretical results are executed.

Distribution of the laminar phases in the case of type­i intermittency with noise

This work is devoted to the intermittent behavior caused by the interplay between the dynamical mechanisms resulting in the type­I intermittency and the stochastic processes. The analytical consideration of the laminar phase distribution is given.

Methods of measuring chaotic synchronization

Different universal methods of calculation of index of chaotic synchronization are considered. One of the methods, which is based on mutual coherence function, is presented in more detail. Its advantages and disadvantages, sensibility to external noise and distortions are discussed. Application of the algorithm to process of destruction of complete chaotic synchronization in two coupled systems with discrete time are demonstrated.

Modeling from time series and applications to processing of complex signals

Signals obtained from most of real­world systems, especially from living organisms, are irregular, often chaotic, non­stationary, and noise­corrupted. Since modern measuring devices usually realize digital processing of information, recordings of the signals take the form of a discrete sequence of samples (a time series). The present paper gives a brief overview of the possibilities of such experimental data processing based on reconstruction and usage of a predictive empirical model of a time realization under study.

Multifractal analysis of digital images

The article is based on the lecture that was given by the first author at the school StatInfo­2009. In the first part the microcanonical variant of multifractal formalism is reviewed. Possibilities for digital image analysis and reconstruction are discussed at the level of technical strictness.

Wavelet-­analysis and examples of its applications

Theoretical background of the wavelet­analysis and a series of applications of the given method are considered including a study of clustering phenomena for synchronous dynamics in structural units if the kidney, tactile information encoding by neurons of the trigeminal complex and detection of information messages from the chaotic carrying signal.

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