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

Прикладные задачи нелинейной теории колебаний и волн

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.

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.

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.

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.

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.

Chaos in radio device with square­law phase modulator and interference amplification of quasi­harmonic signal: a model and simulation

The attempt is undertaken to define a class of oscillations or waves sources, the operation principle of which is based on interference amplification of feedback signal by an input signal. The precedent here is the optical Ikeda’s system. The radio­electronic analog of a nonlinear ring interferometer and it modification are offered, the block diagrams and mathematical models are constructed. The computer simulation is performed. An intermittency, chaos, regular, static modes are detected.

Conformational b–a transition in the model of dna molecule with asymmetric double­well interaction potential of nucleotides

In this paper we consider a modified Peyrard–Bishop model with asymmetric double­well interaction potential of nucleotides and dissipation. It is shown that at the certain value of dissipation coefficient the model solution takes the form of a kink. In terms of DNA molecule it describes the transition between two stable conformational states of DNA molecules – B–A transition.

Noise-­induced phase transitions in competition processes in the external fluctuated media

The influence of external additive homogeneous isotropic field of Gauss fluctuations to evolution of competition processes, which described by Lotka–Volterra equations, where taking into account the mobility of weak population individuals and spatial and temporal fluctuations of resource, has been researched. The numerical simulation of considered model was performed.

Analysis of stochastic work of the composite voltage stabilizer consisting of two buck converters connected as master–slave by fractal measures of deterministic chaos.

Stochastic operation of the parallel–connected buck convertors is considered. For qualitative analysis of the system the bifurcation diagrams are plotted. Quantitative analysis of chaotic regimes was realized by computing of main and special fractal dimensions.

New approach to numerical research of the concrete dynamic systems by methods of pattern recognition and statistical modelling

In the present work the new approach to numerical research of the concrete multi­dimensional and multiparametric dynamic systems is submitted. The offered approach, in part realized and approved, is based on computer calculation of phase trajectories and on use of pattern recognition methods.