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## Call for Papers

 Call for Papers: Special Issue dedicated to the memory of Professor Alexey V. BorisovThe special issue will be emphasize the topics greatly influenced by Professor Alexey V. Borisov, co-founder and co-editor-in-chief of the Russina Journal of Nonlinear Dynamics. The deadline for submission of manuscripts is October 1, 2021. Publication of the issue is provisionally scheduled for December 2021.

# Vol. 17, no. 2

 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 quasi-two-dimensional 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 self-organization 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. Keywords: lateral superlattices, bifurcation-based device, spontaneous transverse electric field, nonequilibrium phase transitions, symmetry breaking of magnetic-field-induced macrostates, resonant enhancement of even harmonics Citation: Maglevanny I. I.,  Smolar V. A.,  Karyakina T. I., Effects of a Perpendicularly Applied Magnetic Field on Harmonically Driven Quasi-two-dimensional Electron Gas: the Static Macrostates Symmetry Breaking and Generation of Even Harmonics in System Output, Rus. J. Nonlin. Dyn., 2021, Vol. 17, no. 2, pp. 141-156 DOI:10.20537/nd210201
 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 saddle-focus 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. Keywords: Shilnikov bifurcation, spiral chaos, Lyapunov analysis Citation: Bakhanova Y.,  Bobrovsky A.,  Burdygina T.,  Malykh S., On the Organization of Homoclinic Bifurcation Curves in Systems with Shilnikov Spiral Attractors, Rus. J. Nonlin. Dyn., 2021, Vol. 17, no. 2, pp. 157-164 DOI:10.20537/nd210202
 Kuryzhov E.,  Karatetskaia E.,  Mints D. Abstract We consider the system of two coupled one-dimensional 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 period-doubling bifurcations. For two coupled parabola maps we focus on studying attractors of two types: those which resemble the well-known discrete Lorenz-like 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. Keywords: strange attractor, discrete Lorenz attractor, hyperchaos, discrete Shilnikov attractor, two-dimensional endomorphism Citation: Kuryzhov E.,  Karatetskaia E.,  Mints D., Lorenz- and Shilnikov-Shape Attractors in the Model of Two Coupled Parabola Maps, Rus. J. Nonlin. Dyn., 2021, Vol. 17, no. 2, pp. 165-174 DOI:10.20537/nd210203
 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. Keywords: autoassociative Hamming network, Hopfield network, iterative algorithm, pattern recognition, dynamical system, neurodynamics, attractors, stationary states Citation: Antipova E. S.,  Rashkovskiy S. A., Autoassociative Hamming Neural Network, Rus. J. Nonlin. Dyn., 2021, Vol. 17, no. 2, pp. 175-193 DOI:10.20537/nd210204
 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. Keywords: hydraulic device, mathematical model, numerical simulation, Godunov’s method, Mie – Grüneisen equation of state, water, weakly compressible fluid approach, incompressible fluid Citation: Raeder T.,  Tenenev V. A.,  Chernova A. A., Incorporation of Fluid Compressibility into the Calculation of the Stationary Mode of Operation of a Hydraulic Device at High Fluid Pressures, Rus. J. Nonlin. Dyn., 2021, Vol. 17, no. 2, pp. 195-209 DOI:10.20537/nd210205
 Kaskov S. I. Abstract This paper presents the results of numerical investigation, calculation analysis and experimental study of heat exchange in a system of plane-parallel 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. Keywords: vortex enhancement, heat transfer, cooling of power electronics Citation: Kaskov S. I., Calculation and Experimental Study of Heat Exchange in a System of Plane-Parallel Channels with Surface Intensifiers, Rus. J. Nonlin. Dyn., 2021, Vol. 17, no. 2, pp. 211-220 DOI:10.20537/nd210206
 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. Keywords: dynamical systems, Buslaev’s countour network, spectral cycles, self-organization Received Citation: Yashina M. V.,  Tatashev A. G., A Two-Contour System with Two Clusters of Different Lengths, Rus. J. Nonlin. Dyn., 2021, Vol. 17, no. 2, pp. 221-242 DOI:10.20537/nd210207
 Abstract Citation: In memory of Alexander V. Karapetyan, Rus. J. Nonlin. Dyn., 2021, Vol. 17, no. 2, pp. 243-244 DOI:10.20537/nd210208