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

Applied Problems of Nonlinear Oscillation and Wave Theory

Nonlinear dynamics of the formation of a spatially inhomogeneous structure in pin diode

The paper presents the results of experimental investigation of stationary distributions of the electric field and the charge carrier concentration in the PIN diode. The investigations have been carried out by use of near­field scanning microwave microscope. Numerical calculations of these values have been performed taking into account the dependence of the mobility and the diffusion coefficient of electrons and holes on the electric field. The alternating maxima and minima form of the field distribution near the contacts and the conductivity has been demonstrated.

Using arduino platform in the measurements and the physical experiment

This paper discusses the possibility of a hardware­software platform Arduino, as a relatively simple and flexible tool that could occupy a niche in the research tools. Radiophysical chaotic oscillator with delayed feedback was created on the base of Arduino.

Investigating nonlinear granger causality method efficiency at strong synchronization of systems

Detecting the direction of coupling between systems using records of their oscillations is an actual task for many areas of knowledge. Its solution can hardly be achieved in case of synchronization. Granger causality method is promising for this task, since it allows to hope for success in the case of partial (e.g., phase) synchronization due to considering not only phases but also amplitudes of both signals.

Structurally complex boundary with specular­diffuse reflection indicatrix

The way of modeling of specular­diffuse character of light reflection from real surfaces is proposed in the paper. Model of structurally complex reflecting boundary baseson the open billiards. Indicatrix of reflection from this surface for all angles of incidence consists only of specular pike and diffuse component. Dependence of the share of specular component on an angle of incidence may be any predefined function, its choice also defines the shape of diffuse component.

Influence of a flexural deformation of a tool on self-organization and bifurcations of dynamical metal cutting system

In the article we offer to consider case of a flexural deformation shifts of a tool when they are essential for nonlinear dynamics of cutting process. This situation is observed for drill deep  holes, because a boring bar has a small values of a flexural stiffness. In that case an angle of cutting  edge reduces and cutting forces increase if the deformation shifts also increased in velocity  direction. The last circumstance becomes occasion for positive feedback that essentially changes  dynamics of the cutting process.

Self-organization and bifurcations of dynamical metal cutting system

The problems of nonlinear dynamics of cutting metal are considered in the article. We offer mathematical model of dynamical system that includes a dynamical relation of the cutting process by using turning example. Basic positions of the dynamical relation are the forces dependence of cutting area, the force’s delay of elastic deformation shift of a tool by relative to workpiece, limitations of the cutting forces on clearance face of the tool, dependence of the cutting forces of the cutting velocity.

Spectrum of semicondactor laser autodyne at focusing radiation

Simulation of autodyne signal at different feedback level influence on measurement of parameters of vibrating reflector has been performed at different values of optical power radiation returned in laser resonator. It has been shown that the spectrum of autodyne signal is enrichment when focusing level is increased.

Analysis of attractors for stochastically forced «predator–prey» model

We consider the population dynamics model «predator–prey». Equilibria and limit cycles of system are studied from both deterministic and stochastic points of view. Probabilistic properties of stochastic trajectories are investigated on the base of stochastic sensitivity function technique. The possibilities of stochastic sensitivity function to analyse details and thin features of stochastic attractors are demonstrated.

Variety of synchronous regimes in ensembles of nonidentical oscillators: Chain and lattice

We study synchronization in one- and two-dimentional ensembles of nonidentical Bonhoeffer–van der Pol oscillators. Small chains (number of elements N <= 4) are proved to have not less than 2 N−1 coexisting stable different synchronous regimes. The chain of N elements is supposed to have not less than 2 N−1 synchronous regimes at the same values of parameters. Formation of synchronization clusters at weak coupling is shown. Regimes, provided by existing of waves, setting rhythm for all elements in ensemble, are investigated.

Variety of synchronous regimes in ensembles of nonidentical oscillators: two coupled elements

We study synchronization of two coupled nonidentical Bonhoeffer–van der Pol oscillators. Coexistence of two different synchronous regimes is proved. Mechanisms of synchronous regimes origination and destruction are investigated. Fluctuations influence on syncronous regimes is considered. It is found that noise can cause: i) synchronization destruction and beating originations; ii) fluctuations-caused bistability destruction; iii) fluctuations-caused intermittency of synchronous regimes without synchronization destruction.


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