# 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 di?erence equation excitation waveguides. The validity of the linear theory and developed a universal characteristic equation of electron waves, using the di?erence equation excitation waveguides in stopbands of slow-wave systems.

## Determining the value of the structure water-containing environment of living tissue in biomedical radio-electronic nanotechnologies millimetric and terahertz ranges

The article contains the short review of the main results on research of a role of structuration of the water-containing environment in the living tissues. These tissues are used as the objects of research in biomedical radio-electronic nanotechnologies of the extremely high-frequency and terahertz ranges. The experimental devices and technique of researches of the water containing environment structuration under the in?uence of electromagnetic radiation are described. The results of pilot studies are given.

## About current state high frequency vacuum electronic and microelectronic devices with field emission

Some results of researches and development of devices with ?eld emission (TWT, BWO, carcinotrode, klystrons and X-ray tubes, ?eld emission displays, etc.) have been brie?y presented in the article. Lines of development of its theory have been designated. Also the vacuum microwave electronics programs o?ered in Europe and USA have been considered. They are directed on using new technologies in coping with the terahertz frequency range, re?ecting the trend of recent years.

## Terahertz vacuum electromagnetic radiation sources: evolution zigzag from klynotron to klynoorbictron

Investigation and development of e?cient electromagnetic oscillations sources are one of the topical issues in the ?eld of terahertz radiophysics and electronics. A frequency region is regarded as an explored for which oscillating, amplifying and measurement devices have not been developed. The exploration of the terahertz frequency range is at the initial state. In a review paper, published in one of the USA scienti?c journal [1], which was devoted to the terahertz radiation vacuum sources there is some reminder of using, a «klynotron e?ect» in the BWO developed at the IRE NASU.

## 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 di?raction 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, di?raction radiation in conditions of channeling, di?raction radiation of a relativistic oscillator, induced radiation in multidimensional space-periodic resonators (natural or arti?cial (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. • 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.

## 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.

## 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.