Browsing by Author "Volkova, Svetlana A."
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Item Discrete Processes and Chaos in Systems of Ordinary Differential Equations(Oles Honchar Dnipro National University, Dnipro, Ukraine, 2022) Belozyorov, Vasiliy Ye.; Volkova, Svetlana A.ENG: A method for constructing a one-dimensional discrete mapping describing a certain periodic process in a general system of ordinary autonomous differential equations is proposed. The resulting discrete mapping is then used to prove the existence of chaos in the original system of differential equations.Item Dynamics of the Interbank Exchange using Neural Technologies(Scientific Publishing Center “Sci-conf.com.ua”, Lviv, Ukraine, 2022) Volkova, Svetlana A.; Anofriev, Pavlo G.; Hiliavskyi, DenysENG: Artificial intelligence is used to predict various events. Recently, the direction of predicting the exchange rate of bitcoin in pair with the dollar has been actively developing. Due to volatility, it is very difficult to predict the price of cryptocurrency. Recurrent neural network are proposed in the work.Item Odd and Even Functions in the Design Problem of New Chaotic Attractors(World Scientific Publishing Company, Singapore, 2022) Belozyorov, Vasiliy Ye.; Volkova, Svetlana A.ENG: Let A ⊂ Rn be a chaotic attractor generated by a quadratic system of ordinary differential equations x˙ = f(x). A method for constructing new chaotic attractors based on the attractor A is proposed. The idea of the method is to replace the state vector x = (x1,...,xn)T located on the right side of the original system with new vector u(x); where u(x) = K ·(h1(x1),...,hn(xn))T , K ∈ Rn×n, and hi(xi) are odd power functions; i = 1,...,n. (In other words, a state feedback x → u(x) is introduced into the right side of the system under study: x˙ = f(x) → x˙ = f(u(x)).) As a result, the newly obtained system generates new chaotic attractors, which are topologically not equivalent (generally speaking) to the attractor A. In addition, for an antisymmetric neural ODE system with a homoclinic orbit connected at a saddle point, the conditions for the occurrence of chaotic dynamics are found.Item Role of Logistic and Ricker’s Maps in Appearance of Chaos in Autonomous Quadratic Dynamical Systems(Springer Netherlands, 2016) Belozyorov, Vasiliy Ye.; Volkova, Svetlana A.EN: New existence conditions of a chaotic behavior for wide class of (n+1)-dimensional autonomous quadratic dynamical systems are suggested. It is shown that in all such systems the chaotic dynamics is generated by 1D discrete map by some combination of the logistic map f (x) = λx(1−x);λ> 0 and Ricker’s map g(x) = x exp(μ−x);μ>0.Item Singular Differential Equations and their Applications for Modeling Strongly Oscillating Processes(Oles Honchar Dnipro National Universuty, Dnipro, Ukraine, 2023) Belozyorov, Vasiliy Ye.; Volkova, Svetlana A.; Zaytsev, Vadym G.ENG: The normal system of ordinary differential equations, whose right-hand sides are the ratios of linear and nonlinear positive functions, is considered. A feature of these ratios is that some of their denominators can take on arbitrarily small nonzero values. (Thus, the modules of the corresponding derivatives can take arbitrarily large value.) In the sequel, the constructed system of differential equations is used to model strongly oscillating processes (for example, processes determined by the rhythms of electroencephalograms measured at certain points in the cerebral cortex). The obtained results can be used to diagnose human brain diseases.Item Study of the Dynamics of Product Sales Process with the Help of Zolotas Model(Oles Honchar Dnipro National University, Dnipro, 2024) Belozyorov, Vasiliy Ye.; Volkova, Svetlana A.ENG: . A new mathematical model describing the dynamics of sales of goods on the market has been proposed. This model takes into account the following characteristics: the average welfare of buyers, the maximum welfare of buyers, the number of buyers who know about the incoming product and the level of market saturation with this product. Examples demonstrating the features of the constructed model are given.Item Substantiation of the Parameters of the Bench for Testing of Railway Wheels for Contact and Fatigue Strength(Technologija, Kaunas, 2022) Raksha, Serhii V.; Anofriev, Pavlo G.; Kuropiatnyk, Oleksii S.; Glavatskij, Kazimir Ts.; Bohomaz, Volodymyr M.; Posmitiukha, Oleksandr P.; Volkova, Svetlana A.ENG: Strength indicators are important parameters of the railway wheels, as they determine the allowable service life of both the wheel itself and the wheelset as a whole. Therefore, the development of bench equipment that allows in the laboratory to reproduce or simulate the real conditions of the wheel load in order to conduct strength tests, is an urgent scientific and practical task. The purpose of this work is to substantiate the parameters of the bench for testing railway wheels for fatigue and contact strength. As the bench has to test railway wheels for fatigue and contact strength at the same time, the requirements of various normative and methodological documents, which determine the procedure for conducting such tests on separate benches, were combined when determining the parameters of the bench. We determined that the working force of the bench should vary from 10% to 100% of the wheel endurance limit, the duration of the tests should correspond to five million load cycles with a frequency of 5 to 10 Hz. To reduce the duration of the tests, pushing on the wheel was carried out by several rollers, which were evenly distributed around the wheel. For the proposed bench, we obtained the dependence that connects the parameters of the test wheel, the parameters of the bench, the wheel pair axle load and the wheel material endurance limit. The results of this study can be used as a basis for the development of new schemes of benches for railway wheels tests.