ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

Applied Problems of Nonlinear Oscillation and Wave Theory

Waveguide with thin nonlinear walls

Characteristics of modes of the planar waveguide with thin walls, which are made from nonlinear media, are studied. The effect of the conversion of a mode from one set to another is considered. This effect may occur if parameters of the waveguide or transmitted power are varied. It is shown that the effect of the guided or leaky modes «disappearance» can arise when the field amplitudes increase, i.e., high powers launched into such a structure can suppress the modal propagation. 

Stochastic sensitivity of limit cycles for «predator – two preys» model

We consider the population dynamics model «predator – two preys». A deterministic stability of limit cycles of this three-dimensional model in a period doubling bifurcations zone at the transition from an order to chaos is investigated. Stochastic sensitivity of cycles for additive and parametrical random disturbances is analyzed with the help of stochastic sensitivity function technique. Thin effects of stochastic influences are demonstrated. Growth of stochastic sensitivity of cycles for period doubling under transition from order to chaos is shown.

Synchronizing the period-­2 cycle in the system of symmetrical coupled populations with stock–recruitment based on the Ricker population model

We investigated coupled map lattices based on the Ricker model that describes the spatial dynamics of heterogeneous populations represented by two connected groups of individuals with a migration interaction between them. Bifurcation mechanisms in­phase and antiphase synchronization of multistability regimes were considered in such systems. To identify a synchronization mode we introduced the quantitative measure of synchronization.

Dynamics of small groups of interacting nephrons in normal and renal hypertension states

Based on the wavelet-analysis of experimental data, we study in this paper the phenomenon of synchronization of oscillations in the dynamics of small groups of structural units of the kidney (paired nephrons and triplets). Distinctions between synchronous dynamics of interacting nephrons in normal and hypertensive rats are discussed. We show that mean duration of synchronous oscillations is about 3 times less in hypertensive rats.

Role of model nonlinearity for granger causality based coupling estimation for pathological tremor

Estimating coupling between systems of different nature is an urgent field of nonlinear dynamics method application. This work aims to compare classical linear Granger approach and its nonlinear analogues based on analysis of ethalon dynamical systems and neurophysiological data. The results achieved show nonlinear approach to be more sensitive, and so it is able to detect significant coupling, when linear one fails.

Nonlinear dynamics of a ring of two coupled phase locked loops

Nonlinear dynamics of the ensemble consisting of two phase­locked generators, which are coupled in a ring with feedback, is discovered. The conditions of stability of the synchronous regimes and appropriatenesses of excitation and progress of the non­synchronous regimes are examined within the bounds of the dynamic model with one and a half degrees of freedom. The extensive image of the dynamic regimes and bifurcating transitions, creating resources for the formation in the system of various types of oscillations, is discovered.

Laser autodyne measurements of ear-drum displacement caused by change of sound pressure level

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.

Dynamical regimes and nonlinear phenomena in generator with frequency-phase control

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.

Detection of information signals based on reconstruction of dynamical systems and discrete wavelet-transform

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.

Pulsed synchronization and synchronization in coupled systems: new aspects of classical problem

Different features of the pulsed synchronization of self-oscillatory systems are considered. Namely nonisochronous, stabilization of the unstable systems, synchronization of the coupled oscillators in the region of the «oscillatory death» and etc. Illustrations for the coupled nonisochronously oscillators and nonidentical (controlling parameter and nonlinear dissipation) oscillators are presented.

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