Applied Problems of Nonlinear Oscillation and Wave Theory

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.

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.

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.

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.

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.

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.

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. In this paper using the etalon test systems with pronounced time scale the method

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.

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.