# Review of Actual Problems of Nonlinear Dynamics

## Two-dimensional distributed feedback as a method for generation of powerful coherent radiation from spatially-extended relativistic electron beams

The purpose of the research presented in the review is to analyze a new feedback mechanism – two-dimensional (2D) distributed feedback, and to study the possibility of using this mechanism for generation of powerful spatially-coherent radiation. Such 2D distributed feedback is implemented by applying 2D Bragg structures, which represent sections of planar or coaxial waveguides with the 2D-periodical corrugation and can be considered as an analog of the 2D photonic crystals. Methods.

## Collective dynamics of networks of active units with pulse coupling: Review

Aim of the paper is to review of collective dynamics study of networks of active units with pulse couplings. Many network oscillatory systems are characterized by interactions between the nodes in the form of an exchange of short signals, or pulses. The most important class of such network systems is biological neural networks, that is, populations of nerve cells. Main approaches to the study of networks with pulse coupling are described and the results obtained to date are systematized.

## On homoclinic attractors of three-dimensional flows

The main goal is to construct a classification of such attractors and to distinguish among them the classes of pseudohyperbolic attractors which chaotic dynamics is preserved under perturbations of the system.

## A brief review of the research results of new methods for generating, transmitting and receiving oscillations and waves based on fractal geometry methods

Purpose of this article is to generalize results of the application of fractal geometry methods in various radiophysic systems and at study of processes occurring in them. Methods. The presentation is built in the form of a brief review of a number of works devoted to new methods for generating, receiving and transmitting signals of various frequency ranges, including microwave frequencies, using fractal geometry approaches.

## Mathematical theory of dynamical chaos and its applications: Review Part 2. Spiral chaos of three-dimensional flows

The main goal of the present paper is an explanation of topical issues of the theory of spiral chaos of three-dimensional flows, i.e. the theory of strange attractors associated with the existence of homoclinic loops to the equilibrium of saddle-focus type, based on the combination of its two fundamental principles, Shilnikov’s theory and universal scenarios of spiral chaos, i.e. those elements of the theory that remain valid for any models, regardless of their origin.

## Reconstruction of model equations of networks of oscillators with delay in node dynamics and couplings between them: Review

The aim of this review is to show the modern level of research in the area of reconstruction of network models from measured time series, for which individual nodes are described by time-delayed equations or there is a delay in coupling. Methods are described for reconstruction of coupling coeﬃcients and functions, nonlinear functions of individual nodes and for detection of superﬂuous couplings. The techniques for delay time detection are considered separately due to their choice is crucial for success of entire reconstruction procedure.

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

Investigation and development of efficient electromagnetic oscillations sources are one of the topical issues in the field 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.

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

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

## 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 influence of electromagnetic radiation are described. The results of pilot studies are given.