Applied Problems of Nonlinear Oscillation and Wave Theory

On the basis of quasi-potential method the stationary distribution of random trajectories in a vicinity of toroidal manifolds of stochastically forced nonlinear systems is investigated. For the quasi-potential approximation the quadratic form defined by some matrix function is used. This function named stochastic sensitivity function characterizes the response of considered system on random disturbances. Construction of this function is reduced to the decision of a boundary problem for linear differential matrix equation.

Dynamics of an ensemble of two parallel phase-locked-loop systems with lowinertia control loops is investigated. Stability of synchronous modes of the ensemble is considered. Mechanisms of arising of quasi-synchronous oscillations are studied. Domains of existence of synchronous, quasi-synchronous, and asynchronous modes are analysed. The results obtained are compared with analogous data of modeling dynamics of an ensemble with cascade coupling; their common features and basic differences are distin- guished.

A new approach to describe and analysis the structural and forming characteristics in time domain of signals are presented here. This approach is based on the decomposition of initial process into individual components, which are characteristic of the structure of its curving, and corresponding calculations for different configuration, energy and information parameters.

А number of novel possibilities of generation and amplification of spatially coherent radiation using planar Bragg structures is reviewed. In particular, we study schemes of Cherenkov oscillators with 2D distributed feedback, and a possibility of using this mechanism for synchronization of radiation of active laser media. Electronic amplifiers based on planar Bragg waveguides are discussed as well.

The possibility of usage of klystron active oscillator with delayed feedback as a source of chaotic radio pulses was explored. Experimental results of chaotic radio pulses producing in multicavity active oscillator with delayed feedback by means of the influence of radio-frequency pulses, delivered in the feedback line are presented. Experimental results showed that the initiation of chaotic radio-frequency pulses is possible in the whole zone of amplitude curve (gain characteristic) of autonomous klystron active oscillator.

Features of nonlinear dynamics of backward-wave tube in the presence of such factors as energy dissipation at wave transmission, field of space charge, wave reflection at the system edges are analyzed. Dynamics of the backward-wave tube with coupled systems including multi-stability connected with possibility of beam interaction with low or fast normal wave in the coupled transmission lines is discussed.

Based on the wavelet-analysis technique, a study is performed of how characteristics of physiological tremor are changed at the influence of a weak low-frequency magnetic field. Different approaches to analyze the structure of experimental data are considered using both, real and complex wavelet-transform basic functions. It is shown that magnetic field has an effect on a local regularity of analyzed processes and on their energy characteristics.

Processes in autonomous 2-D digital recursive filters of first order with three levels of quantization are investigated. Method of bifurcation diagram construction is proposed. With its help conditions of existence of the determine input movements types expressed through coefficients of the filter are found.

Results of experimental investigations of the electrocardiogram change for, patients with nystagmus which decreases during periodic light influence are presented. Forms of electrocardiosignal and its spectrum, Baevsky indexes, nystagmusgrams before-and in the moment of light influence are given. Periodic light influence on the eyes in the moment of nystagmus supression leads to the increase of the tone level, of the sympathetic nervous system in the regulation of the heart activity and simultaneously to the decrease of th noise components of the electrocardiogram spectrum is shown.

Features of the synchronization picture in the system which limit cycle lied in threedimensional phase space are considered. By the example of Ressler system with the periodic sequence of d-Functions it is shown, that the synchronization picture essentially depends on a direction of the external force. Features of the synchronization tongues are found.