Browsing by Author "Zaytsev, Vadym G."
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Item Development of an Approach to Ensure Stability of the Traction Direct Current System(PC "Technology Center", Ukrainian State University of Railway Transport, Kharkov, 2018) Sychenko, Viktor G.; Kuznetsov, Valeriy; Kosariev, Yevhen M.; Hubskyi, Petro V.; Belozyorov, Vasiliy Ye.; Zaytsev, Vadym G.; Pulin, Mykola M.EN: The result of applying the quantitative approach to the calculation of static stability of the traction power system helped us establish that when a train runs along an actual section there emerge zones with lack of stability in terms of voltage. Exact solution to the task of evaluating the stability is extremely difficult because of the need to compute the nonlinear dependences determining the modes of operation of the traction power system and electric rolling stock. In this work, we constructed a system of four autonomous nonlinear differential equations based on experimental data that simulate the behavior of current and voltage in the contact network. We also calculated stability regions for voltage regulators in the traction network, which stabilize voltage at pantographs of electric rolling stock. The obtained stability regions of voltage regulators made it possible to estimate resource of stability and to find the most robust regulators out of those constructed. The study revealed that the non-linear regulator has better robust properties than the linear one. In this case, stability of the linear regulator is very narrow ‒ Δk=0.000004, which is an order of magnitude lower than for the non-linear regulator. When applying the non-linear regulator, voltage in the contact network stabilizes 3 times faster regardless of the place of its location. Application of the devised approach would make it possible to calculate the stability regions for various schematics of the traction network in the implementation of high-speed motion and to narrow the range of voltage fluctuations. The developed dynamic model of power consumption processes, as well as the voltage regulator, could be used when constructing an intelligent, adaptive traction power system for high-speed motion.Item A New Approach to the Problem of Diagnostics of Cerebral Cortex Diseases Using Chaotic Dynamics Methods(Richtmann Ldt, London, 2017) Belozyorov, Vasiliy Ye.; Pohorielov, Oleksii V.; Serdiuk, Valerii N.; Zaytsev, Vadym G.EN: An modeling attempt of behavior process of brain electric impulses for some patient by solutions of 3Dsystem of autonomous quadratic differential equations is undertaken. This system of differential equations was got from a multivariatetimes series with the help of polynomial averages and least squares method. Further, with the help of the got system a question about existence of chaotic attractor in this system is studied. In this case, the presence of chaotic attractor makes it possible to interpretas the absence of disease and vice versa.Item A New Mathematical Model of Dynamic Processes in Direct Current Traction Power Supply System(Дніпровський національний університет ім. О. Гончара, 2019) Belozyorov, Vasiliy Ye.; Kosariev, Yevhen M.; Pulin, Mykola M.; Sychenko, Viktor G.; Zaytsev, Vadym G.EN: Abstract. A new autonomous 4D nonlinear model with two nonlinearities describing the dynamics of change of voltage and current in the contact railway electric network is offered. This model is a connection of two 2D oscillatory circuits for current and voltage in the contact electric network. In the found system for the defined values of parameters an existence of limit cycles is proved. By introduction of new variables this system can be reduced to 5D system only with one quadratic nonlinearity. The constructed model may be used for the control by voltage stability in a direct current power supply system.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.