Applied Problems of Nonlinear Oscillation and Wave Theory

Changes in the dynamics of renal blood flow at the transition from the microscopic level of individual nephrons to the macroscopic level of the whole kidney are investigated. Rhythmic processes caused by the auto-regulatory mechanisms and their interactions in the form of synchronization and modulation are analyzed. Distinctions of the dynamics in the cases of normal and increased arterial pressure are discussed.

The dynamics of quantum wave packets in one-dimensional system with spatially confined quadratic potential, feedback and friction was numerically investigated in the context of the Schrodinger–Langevin–Kostin equation. The coherent oscillations are  possible in the system under determined values of the feedback force and friction coefficient. There are the critical values of these quantities when the packet oscillations become complicated, the uncertainty product increases sharply, oscillates, but the Fourier-spectrum is everywhere dense.

In this paper we consider various networks of mutually coupled identical Hodgkin–Huxley systems. The peculiarities of transition to complete synchronization in networks subjected to suprathreshold periodic driving and common random forcing are examined both theoretically and through numerical simulation. The conditions for global stability of complete synchronization in networks of two «star»-coupled structures are obtained within the framework of connection graph stability method. Various scenarios determining the increase of the number of elements in such ensembles are considered.

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.

The paper deals with a new multi­element processor platform to model the behavior of interacting dynamical systems – active wireless network. Each dynamical system modeling process, is associated with an active network node. The interaction between the dynamical systems is made through the transfer of information on the state of the system through radio channels between nodes of active network. Platform capabilities are demonstrated by an ensemble of oscillators Kuramoto. Describes the technique of modeling, experimental results and their analysis.

The results of measurements of ear-drum longitudinal displacement against vibrations excited by periodical sound pressure have been results. The existence of ear-drum longitudinal displacement with the increase of sound pressure intensity has been txperimentally proved. By spectrum of autodyne signal of semiconductor laser, using the window method of semiconductor laser analysis, by changes of phase of autodyne signal in time the values of such displacement for different levels of sound pressure has been determined.

The paper represents the results of numerical study of dynamical regimes and bifurcation transitions in oscillatory system with frequency-phase control. The study was carried out on the base of mathematical model with three degrees or freedom in cylindrical phase space. Rich variety of various attractors of oscillatory and rotatory type corresponding to modulating modes of the system has been detected. Various scenarios of transition from regular dynamical regimes to chaotic ones under variation of the control loops parameters are analyzed.

An approach to extract transmitted messages from the chaotic carrying signal is proposed based on the combination of dynamical systems reconstruction and the discrete wavelet-transform. It is shown that discrete wavelets allow one to increase the stability to noise of the detecting algorithm that deals with the reconstruction technique.