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The pulse-driven van der Pol oscillator with the external pulse amplitude depending on the system variables is considered. The discrete map for values of the system variables just before the pulse moment was obtained by the slow-varying-amplitude method. Further the parameter space of this map was analyzed, and the existence of the Hamiltonian critical behavior in this system was shown. The remarkable fact is that our system is the system with the dissipation depending not only on the parameter values, but on the variable values too.

In this work the nonlinear dynamics in a chain of unidirectionally coupled gyrobackward wave oscillators is studied. In coupled system, when the control parameters of each distributed system are changed, it is possible to show both a developed chaos dynamics and the regimes of stationary oscillations with one frequency.

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 article is devoted to the problems of history of the Hamiltonian chaos discover  in 1960th which is described a little in publications in comparison with the history  dissipative chaos. The main center of Hamiltonian chaos research was the Nuclear Physi Institute in Novosibirsk where B.V. Chirikov and G.M. Zaslavsky worked, being the maj specialists in the world in this field of science.

Maps having cycles of period two in which Hopf bifurcations of new cycles occur are localized in the family of two-dimensional logistic maps. For the purposes of illustration of the bifurcation property one-dimensional sections of bifurcation diagrams with one fixed parameter for two-parameters’ first-return maps of two-dimensional logistic maps are given.

Hard turbulence, a chaotic mode distinguished by infrequent catastrophic outbreaks on the weak irregular space oscillation background, is considered. On-off intermittency as one of the possible ways of simplified qualitative definition of hard turbulence is discussed. The paper introduces an example solution of the inverse problem, constructing a deterministic-probabilistic system (a channels and jokers system) generating time series with characteristics similar to the ones of the time series generated by a simple system working in on-off intermittency mode (the Ershov mapping).

We examine regimes of magnetron corresponding to the temperature limitation conditions and spatial charge emission limitation under spatially inhomogeneous magnetic field. The magnetic field variation law selection proved to exert influence on noise level in devices of magnetron type with a central cathode.

We present the electronic scheme of generator with inertial nonlinearity on operational amplifiers and field-effect transistors. The amplification coefficient in the generator is determined analytically, it is controlled by a field-effect transistor. The differential equations of the generator are derived strictly and consecutively. In the experiment we show, that the proposed scheme demonstrates the cascade of period-doubling bifurcations of transition to chaos.

The paper discusses the possibilities of studying of rhythmic processes with linearly changed frequencies («chirps») based on the wavelet-analysis. Limitations of the continuous wavelet-transformation in the analysis of superpositions of signals with linear frequency modulation are formulated. Effects of the interference and the modulation of rhythmic processes are considered.