Vol. 17, no. 2
Vol. 17, no. 2, 2021
Maglevanny I. I., Smolar V. A., Karyakina T. I.
Abstract
In this paper, we consider activation processes in a nonlinear metastable system based
on a quasitwodimensional superlattice and study the dynamics of such a system, which is
externally driven by a harmonic force in regimes of controlled instabilities. The spontaneous
transverse electric field is considered as an order parameter and the forced violations of the order
parameter are considered as a response of a system to periodic driving. The internal control
parameters are the longitudinal applied electric field, the sample temperature and the magnetic
field which is orthogonal to the superlattice plane. We investigate the cooperative effects of
selforganization and high harmonic forcing in such a system from the viewpoint of catastrophe
theory It is shown through numerical simulations that the additional magnetic field breaks the
static macrostates symmetry and leads to generation of even harmonics; it also allows the control
of the intensity of particular harmonics. The intensity of even harmonics demonstrates resonanttype
nonmonotonic dependence on control parameters with the maxima at points close to critical
points of the synergetic potential.

Bakhanova Y., Bobrovsky A., Burdygina T., Malykh S.
Abstract
We study spiral chaos in the classical Rössler and Arneodo – Coullet – Tresser systems. Special
attention is paid to the analysis of bifurcation curves that correspond to the appearance of
Shilnikov homoclinic loop of saddlefocus equilibrium states and, as a result, spiral chaos. To
visualize the results, we use numerical methods for constructing charts of the maximal Lyapunov
exponent and bifurcation diagrams obtained using the MatCont package.

Kuryzhov E., Karatetskaia E., Mints D.
Abstract
We consider the system of two coupled onedimensional parabola maps. It is well known
that the parabola map is the simplest map that can exhibit chaotic dynamics, chaos in this map
appears through an infinite cascade of perioddoubling bifurcations. For two coupled parabola
maps we focus on studying attractors of two types: those which resemble the wellknown discrete
Lorenzlike attractors and those which are similar to the discrete Shilnikov attractors. We describe
and illustrate the scenarios of occurrence of chaotic attractors of both types.

Antipova E. S., Rashkovskiy S. A.
Abstract
An autoassociative neural network is suggested which is based on the calculation of Hamming
distances, while the principle of its operation is similar to that of the Hopfield neural network.
Using standard patterns as an example, we compare the efficiency of pattern recognition for the
autoassociative Hamming network and the Hopfield network. It is shown that the autoassociative
Hamming network successfully recognizes standard patterns with a degree of distortion up to
40% and more than 60%, while the Hopfield network ceases to recognize the same patterns with
a degree of distortion of more than 25% and less than 75%. A scheme of the autoassociative
Hamming neural network based on McCulloch – Pitts formal neurons is proposed. It is shown
that the autoassociative Hamming network can be considered as a dynamical system which has
attractors that correspond to the reference patterns. The Lyapunov function of this dynamical
system is found and the equations of its evolution are derived.

Raeder T., Tenenev V. A., Chernova A. A.
Abstract
This paper is concerned with assessing the correctness of applying various mathematical
models for the calculation of the hydroshock phenomena in technical devices for modes close to
critical parameters of the fluid. We study the applicability limits of the equation of state for
an incompressible fluid (the assumption of constancy of the medium density) to the simulation
of processes of the safety valve operation for high values of pressures in the valve. We present
a scheme for adapting the numerical method of S. K. Godunov for calculation of flows of incompressible
fluids. A generalization of the method for the Mie – Grüneisen equation of state is made
using an algorithm of local approximation. A detailed validation and verification of the developed
numerical method is provided, and relevant schemes and algorithms are given. Modeling of
the hydroshock phenomenon under the valve actuation within the incompressible fluid model is
carried out by the openFoam software. The comparison of the results for the weakly compressible
and incompressible fluid models allows an estimation of the applicability ranges for the proposed
schemes and algorithms. It is shown that the problem of the hydroshock phenomenon is correctly
solved using the model of an incompressible fluid for the modes characterized by pressure ratios of
no more than 1000 at the boundary of media discontinuity. For all pressure ratios exceeding 1000,
it is necessary to apply the proposed weakly compressible fluid approach along with the Mie –
Grüneisen equation of state.

Kaskov S. I.
Abstract
This paper presents the results of numerical investigation, calculation analysis and experimental
study of heat exchange in a system of planeparallel channels formed by rectangular fins,
which are applied in a heat removal device using heat tubes for power semiconductor energy converters.
Passive cooling (heat removal by radiation and natural convection) and active cooling
(heat removal by radiation and forced convection) are investigated for various velocities of air
cooling of fins by spherical vortex generators applied to its surface. A comparative analysis of
the results is carried out for the average effective heat removal resistance and for the average
temperature at the ends of the fins. The application of numerical modeling to solve such problems
confirms the effectiveness of computational technologies. The difference between the results
of the study ranges from 10 to 16% depending on the airflow rate.

Yashina M. V., Tatashev A. G.
Abstract
A system belonging to the class of dynamical systems such as Buslaev contour networks is
investigated. On each of the two closed contours of the system there is a segment, called a cluster,
which moves with constant velocity if there are no delays. The contours have two common points
called nodes. Delays in the motion of the clusters are due to the fact that two clusters cannot
pass through a node simultaneously. The main characteristic we focus on is the average velocity
of the clusters with delays taken into account. The contours have the same length, taken to
be unity. The nodes divide each contour into parts one of which has length $d$, and the other,
length 1 − $d$. Previously, this system was investigated under the assumption that the clusters
have the same length. It turned out that the behavior of the system depends qualitatively on
how the directions of motion of the clusters correlate with each other. In this paper we explore
the behavior of the system in the case where the clusters differ in length.
