Review of Actual Problems of Nonlinear Dynamics

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.

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.

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.

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.