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In the work we present a two-stage scheme of optimal correction of the dynamic system’s parameters space aimed at the transformation of the system’s chaotic regime into the regular one through minimal intensity of the perturbation. The offered technique is based on combination of the optimal control theory methods with numerical tests of chaos suppression quality.

Systems of billiard types with perturbed boundaries are described. A generalized dispersing billiard – the Lorentz gas with the open horizon – and a focusing billiard in the form of stadium are considered. It is analytically and numerically shown that, if the billiard possesses the property of the developed chaos, the consequence of the boundary perturbation is the Fermi acceleration. However, the perturbation of the nearly integrable billiard system leads to a new interesting phenomenon – the separation of the billiard particles in their velocities.

The behavior of the Pierce diode has been considered from the point of view of the spatial Lyapunov exponents. The method of calculation of the spectrum of the spatial Lyapunov exponents for the electron spatial extended systems has been proposed. The autonomous dynamics of the Pierce diode as well as the behavior of two unidirectionally coupled Pierce diodes when the generalized synchronization is taken place have been considered.

A comparation of wavelets and empirical modes concepts is performed that represent the most perspective tools to study the structure of nonstationary multimode processes. Their advantages over the classical methods for time series analysis and restrictions of both approaches are discussed that needs to be known for correct interpretation of the obtained results. New possibilities in the study of signals structure at the presence of noise are illuctrated for digital single­channel experimental data of prospecting seismology.

At the autooscillator with small reflection from the remote load the mode stability relative to decay into two side satellites was studied by numerical simulation of characteristic equation. At arbitrary exceed over oscillation threshold the stability regions was founded in the space of system parameters. The results are in a good agree, from the one hand, with theory in the parameter space where characteristic equation can be solved analytically, from the other hand, with the results of numerical simulation of transient processes between modes.

At the autooscillator with weakly reflected remote load the number of one­frequency states –longitudinal modes – increases with the growth of the reflection coefficient and the length of the delay line. A mode of this kind can be unstable in some parameter regions. There can be two types of perturbations: a) the perturbations resulting in a slow evolution of principal mode amplitude and frequency; b) the perturbations in the form of two satellites which frequencies are symmetric from that of the principal mode.

Mathematical model of Volume Free Electron Lasers (VFEL) is described. Some aspects and origins of VFEL chaotic dynamics are examined.

For a typical phase lock loop with the second­order filter and delayed feedback, conditions of appearance and characteristics of regular and chaotic automodulation regimes are studied.

Forced synchronization of self­oscillating system with two degrees of freedom is studied in the case when there are no resonance relations between eigenfrequencies and interaction of the modes has the form of mode competition. Stability conditions for the regimes of one­ and two­frequency oscillations are obtained analytically. The structure of synchronization tongues on the frequency–amplitude of external driving parameters plane is studied numerically. Mechanisms of establishing of the synchronous regime are considered depending on coefficients of non­linear mode coupling.

Periodic external signal effect on the collective dynamics of charge in semiconductor superlattice is studied. It is shown, that periodically­oscillating external electrical field can synchronize the transport of domains of the high density of charge as well as oscillations of electrical current flowing through the superlattice.