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By the example of the quasi-periodically forced logistic map we investigate statistical properties of the transition from strange nonchaotic attractor to chaos in the system with intermittent dynamics. The probability characteristics of laminar and chaotic phase distributions, as well as scaling laws for distributions of local Lyapunov exponents are studied at parameter values near the transition point.

 We present a method and results of numerical computations on verification of hyperbolic nature for the chaotic attractor in a system of two coupled nonautonomous van der Pol oscillators (Kuznetsov, Phys. Rev. Lett., 95, 2005, 144101). At selected parameter values, we indicate a toroidal domain in four-dimensional phase space of Poincar´ e map (topologically, a direct product of a circle and a three-dimensional ball), which is mapped into itself and contains the attractor we analyze.

Bifurcational mechanizms of multistability formation on base of regimes of antiphase synchronization in diffusivelly coupled cubic maps are considered. Bifurcations of periodic orbits inside symmetric invariant subspace, which containes attractors of synchronous oscillations, are studied.

Bifurcational mechanisms responsible for destruction of antiphase synchronization of chaos are studied. Two cubic discrete maps with symmetric diffusive coupling and additional control term are used as a model. Phenomenon of synchronization formation and destruction are explored in connection with bifurcations of principal periodic orbits embedded in the chaotic attractor.

Stable and unstable regimes of glycerine convection in vertical toroidal loop are investigated experimentally. The results of Fourier-analysis, DFA, wavelet-, and correlation analysis of liquid’s motion peculiarities are presented. Chaotic attractor with Lorenz-attractor signs is constructed.

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.

In the work nonlinear Duffing oscillator is considered under impulse excitation with two ways of introduction of the random additive term simulating noise, - with help of amplitude modulation and modulation of period of impulses sequence. The scaling properties both in the Feigenbaum scenario and in the tricritical case are shown.