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

Review of Actual Problems of Nonlinear Dynamics

By the theory of the electron waves and the discrete electron-wave interaction in the stopbands of the slow-wave systems

The role of the discrete description of electron-wave interaction in high-power traveling wave tubes is shown. Deals with the development of this trend on the basis of the theory of interaction of the difference equation excitation waveguides. The validity of the linear theory and developed a universal characteristic equation of electron waves, using the difference equation excitation waveguides in stopbands of slow-wave systems.

Radiative processes, radiation instability and chaos in the radiation formed by relativistic beams moving in three-dimensional (two-dimensional) space-periodic structures (natural and photonic crystals)

We review the results of studies of spontaneous and stimulated emission of relativistic particles in natural and photonic crystals. We consider the diffraction of electromagnetic waves in a crystal, and the resonance and parametric (quasi-Cherenkov) X-ray radiation, the radiation in the channeling of relativistic particles in crystals, diffraction radiation in conditions of channeling, diffraction radiation of a relativistic oscillator, induced radiation in multidimensional space-periodic resonators (natural or artificial (electromagnetic, photonic) crystals).

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.

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 wavelet-based methods in geophysics is also 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 electron-positron 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 non-Markovian 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 type-I 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.

Multifractal analysis of digital images

The article is based on the lecture that was given by the first author at the school StatInfo-2009. 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 it's 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.