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

chaotic attractor

On methods for verification of the pseudohyperbolicity of strange attractors

The topic of the paper is strange attractors of multidimensional maps and flows. Strange attractors can be divided into two groups: genuine attractors, that keep their chaoticity under small perturbations, and quasi-attractors (according to Afraimovich–Shilnikov), inside which stable periodic orbits can arise under small perturbations. Main goal of this work is to construct effective criteria that make it possible to distinguish such attractors, as well as to verify these criteria by means of numerical experiments.

On homoclinic attractors of three-dimensional flows

The main goal is to construct a classification of such attractors and to distinguish among them the classes of pseudohyperbolic attractors which chaotic dynamics is preserved under perturbations of the system.

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.

Complex dynamics and chaos in electronic self-oscillator with saturation mechanism provided by parametric decay

We consider an electronic oscillator based on two LC-circuits, one of which includes negative conductivity (the active LC-circuit), where complex dynamics and chaos occur corresponding to the model of wave turbulence of Vyshkind–Rabinovich. The saturation effect for the self-oscillations and their chaotisation take place due to parametric mechanisms due to the presence of a quadratic nonlinear reactive element based on an operational amplifier and an analog multiplier.