Кафедра електричної інженерії (ІПБТ)

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UK: Кафедра електричної інженерії (Інститут промислових та бізнес технологій, ІПБТ) EN: Department of Electrical Engineering (IIBT)

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Analysis of Operational Characteristics of SRM in Emergency Modes of the Converter Unit
(IEEE, 2022) Vlasenko, Vladimir; Tytiuk, Valerii; Kuznetsov, Vitalii V.; Kuntush, Yelena; Chornyi, Oleksii; Busher, Victor
ENG: The paper analyzes the issues of maintaining the operability of a switched reluctance motor (SRM) in various emergency situations. The researches were carried out using simulation modeling in the Matlab environment, the developed model was used for both normal and emergency operation modes. A series of dynamic tests of the motor torque has been carried out, and the values of the electromagnetic torque pulsation coefficient have been calculated. The possibility of maintaining the operability of SRM in the event of various emergency situations in the phases of the motor has been proved. The static mechanical characteristics of the motor are built and the calculation of the droop of the mechanical characteristics for possible emergency modes is performed. © 2022 IEEE.
Analysis of the Neutral Grounding Modes Influence on the Reliability Characteristics of Local Systems with Renewable Energy Sources
(Polskie Towarzystwo Diagnostyki Technicznej, Warszawa, 2021) Ostapchuk, Oleksandr; Kruczek, Włodzimierz; Kuznetsov, Valeriy; Kuznetsov, Vitaliy; Tsyplenkov, Dmytro
ENG: When comparing the performance indicators of electrical networks with different types of neutral grounding, along with the fulfilment of the requirement to ensure reliability of power supply to consumers, serious attention is drawn to the main network parameters influencing the performance of power supply systems. Analysis of research and its results, reported above, on the influence of the neutral ground of power networks on the reliability and electrical safety conditions of the power supply systems as a whole, on the damage of distribution networks and electrical equipment as well as on the working capacity of relay protection devices, provides an opportunity to estimate each specific operation mode of the neutral and to develop recommendations aimed at strengthening the positive indicators of the corresponding modes. Other things being equal, reliability of power supply to electrical receivers or reliability of distribution networks is mainly determined by the damage to network elements and the performance of relay protection devices. The degree of influence of these factors on the reliability of distribution networks depends on the neutral mode, which in turn determines the level of overvoltages and the nature of transient processes at ground failure.
Coefficient of Local Loss of Mechanical Energy of the Flow for a Mixture of Charge Materials
(Dnipro University of Technology, 2021) Selegej, Andriy Mikolayovich; Ivaschenko, Valeriy; Golovko, Vjacheslav Iljich; Kiriya, R.; Kvasova, Luydmila Sergijvna
ENG: Purpose. To determine the dependence of the coefficient of local losses of mechanical energy of flow of a twocomponent mixture of charge material on its depth, content of components, and average equivalent diameter of particles in the case of their freedispersed motion. Methodology. The value of the coefficient of local losses of mechanical energy was determined by the value of the hydraulic resistance of the fluid during its movement in open channels and pipes. In this paper, methods were used of comparative analysis, mathematical modeling and forecasting of dynamic processes in the flow of granular material. findings. Based on the results of theoretical studies, a mathematical model was obtained, the use of which allows calculating the coefficient of local losses of mechanical energy for the flow of a twocomponent mixture of charge materials with agglomerate particle sizes from 15 to 50 mm, pellets from 6 to 12 mm, coke from 10 to 60 mm. The developed model with satisfactory accuracy makes it possible to evaluate the movement of the charge from the indicated materials along the paths of the charging devices of blast furnaces at a speed in the range from 1.5 to 20 m/s and to determine the trajectories of the mixture of charge materials on the top with an accuracy of 0.2 m. It is noted that the calculation of the above coefficient by the known techniques is not accurate enough, which is associated with the uncertainty in the choice of a single average equivalent diameter of the particles of the two component charge. Comparative analysis of the developed model with the known models and experimental data indicates that the accuracy of calculating the dynamic parameters of a twocomponent flow of charge materials using the developed model increases by 5–10 % in comparison with calculations using the previously known models. Originality. For the first time, regularities of changes in the coefficient of internal mechanical losses of a twocomponent flow of charge materials from its depth, content of components, average equivalent particle diameters when moving along the paths of charging devices of blast furnaces have been established. practical value. Mathematical dependencies have been developed and can be used to determine the technological parameters of the charge of a modern blast furnace with different characteristics of the granulometry of the charge and the ratios of its components. This will increase the accuracy of predicting the course of the process under consideration, the degree of automation of the control systems for the technological process of the charge supply of blast furnaces, will make it possible to use expensive charge materials more efficiently, reduce energy consumption and reduce the harmful impact on the environment.
Complex of Mathematical Models and Methods to Calculate Pressure Effect on Sulfide Distribution in Steel
(Хмельницький національний університет, Україна, 2021) Selivyorstova, Tetjana V.; Selivyorstov, Vadim Yu.; Kuznecov, Vitaliy V.
ENG: Primary objective is to develop computational method to analyze digital pictures of sulfide prints, helping obtain qualitative image characteristics, and to formulate mathematical model of the distribution of sulphide inclusions to determine specific features of the pressure effect on the macrostructure formation of carbon steel castings flooded into the uncooled mold. The research was carried out using images of sulfide prints of templates cut of steel cylindrical castings; L500 steel was applied. The castings result from industrial tests of a method of gas-dynamic effect on the fusion in the foundry forms under the conditions of a casthouse of Dnipropetrovsk aggregate plant PJSC. Digital pictures of sulfide prints, obtained in terms of the increased rate of gas pressure and maximum pressure, were binarized; defective fra gments were removed; and zo ning took place. The developed computational method has been applied for fragments of images, representing different zones; data arrays have been received containing sizes and amounts of inclusions in the fragment. The developed computational method to analyze digital images of sulfide prints has been implemented. ASImprints software support has helped obtain qualitative characteristics of images; namely, distribution of amount of the certain-size sulfide inclusions. The computational method to analyze digital images of sulfide prints has made it possible to study the set of patterns of sulfide prints. The dependences have been obtained, describing specific features of sulfide inclusion distribution while varying gas-dynamic pressure method in terms of fusion in the casting form. It has been demonstrated that the distribution describes effectively the power-series distribution to compare with the exponential one. Mathematical model of the power -series distribution parameter dependence upon pressure has been developed. Deviation of the distribution parameters in terms of the experimental values and the model values has been evaluated. The research demonstrates the ways to apply an algorithm of simple recursive casting for quantitative analysis of digital images of sulfide prints. Use of ASImprints, being software implementation of the computational method to analyze digital images of sulfide prints making it possible to obtain qualitative characteristics of images, has helped identify that the increased pressure within a casting-device for gas injection system results in the increased specific amount of inclusions and the decreased specific zone of sulfide inclusions respectively. It has been defined that exponential function describes reliably the nature of sulfide inclusion distribution in the digital image of sulfide print. The research has demonstrated that fragments of a sulfide print, belonging to one zone, are statistically homogeneous. Thus, it is possible to analyze quantitively digital image zone of a sulfide print on its fragment. Mathematical model of dependence of sulfide inclusion distribution in carbon-steel castings in terms of gas-dynamic effect on fusion solidifying in a mold has been developed. The model may be applied to predict sulfide inclusion distribution within the selected zones of cross section of the cylindrical castings solidifying in the uncooled mold in terms of the preset mode of gas-dynamic effect.
Development of a Method of Calculating the Temperature of a Survey Assembly When Preparing a Train Dispatch
(Львовский политехнический национальный университет, Львів, 2020) Ustymenko, Dmytro V.; Kuznetsov, Vitaliy; Marenych, Oksana L.; Kovzel, Maksim; Mukha, Andrii M.; Sinkevych, Oleksiy; Tryputen, Mykola; Al Said Ahmad, Mohammad Ahmad Diab
ENG: The features of the thermal state of the current collection unit «contact wire – contact insert of the current collector» in the conditions of preparation of electric rolling stock for the journey are considered. As part of the study, a methodology has been developed for estimating the heating temperature of the power sliding contact zone in the conditions of train preparation for journey. Application of the method will help to reduce the number of «burnouts» of the contact wire due to the exact selection of the heating/cooling time of the train for a certain heating/conditioning current when preparing the electric rolling stock for the journey. It was established that the cause of the «burns» of the contact wire in the parking lots when preparing the train dispatch is the excess of the permissible temperature of the power sliding contact as a result of the prolonged action of the heating/conditioning current. The standard approach for determining the duration of heating is based on the average values of the loads on the system and therefore does not take into account some factors, for example, the state of the contact wire, the state of the contact insert of the current collector, the number of cars in the train, and so on. The proposed technique is based on the classical theory of electrical contact and the theory of heating a homogeneous body, which makes it possible to accurately assess the thermal state of the power sliding contact and convenient enough for use in operating conditions. The results of the work are of practical value, since the technology of preparing a train for dispatch can be supplemented by calculating the contact temperature «contact wire element – contact insert element» in accordance with the proposed methodology. This will allow for a specific train in specific conditions to apply a set of measures to prevent «burnout» of the contact wire in the event of a possible temperature exceeding the permissible value.
Development of Mathematical Models of Energy Conversion Processes in an Induction Motor Supplied from an Autonomous Induction Generator with Parametric non-Symmetry
(НВП ПП «Технологічний Центр», Харьків, 2021) Chenchevoi, Volodymyr; Kuznetsov, Valeriy; Kuznetsov, Vitalii; Zachepa, Iurii; Chencheva, Olga; Chornyi, Oleksii; Kovzel, Maksim; Kovalenko, Viktor; Babyak, Mykola O.; Levchenko, Serhii
ENG: The paper presents studies of the system “induction generator-induction motor” with parametric asymmetry on a mathematical model to determine the quality of generated electricity in load operating modes. A mathematical model of the “induction generator-induction motor” system has been developed taking into account losses in steel and parametric asymmetry. The analysis of the transient characteristics of an induction generator when a motor load is connected in symmetrical and asymmetrical modes of operation is carried out. The results of changes in the main characteristics of an induction motor at various degrees of parametric asymmetry in the generator are presented. The quality of the generated electricity was analyzed based on the calculations of the unbalance coefficients for each of the operating modes. The assessment of the thermal state in steady-state conditions was carried out using an equivalent thermal equivalent circuit. Thermal transients were investigated when starting an induction motor from an autonomous energy source based on an induction generator. On a thermal mathematical model, the study of the effect of the output voltage asymmetry on the heating of the connected induction motor was carried out. It is shown that the asymmetry of the output voltage of an induction generator reaches 3–10 % and causes overheating of the windings in excess of the permissible values. A regression model has been developed for studying the operating conditions of an induction motor when powered by an induction generator with an asymmetry of the stator windings. The use of the obtained equations will make it possible to determine the most rational combination of factors affecting the heating of the stator windings of induction machines, in which they will not overheat above the maximum permissible temperature values of the corresponding insulation classes.
Development of the System of Initial Excitation of the Autonomous Induction Generator
(Springer, Singapore, 2022) Chenchevoi, Volodymyr; Kuznetsov, Valeriy; Zachepa, Iurii; Chornyi, Oleksii; Chencheva, Olga; Kuznetsov, Vitaliy V.; Yatsiuk, Rostyslav; Luhova, Olha
ENG: The article defines the conditions of self-excitation of an inductive generator with capacitor excitation as part of an autonomous power source. Recommendations for the design of an autonomous power source based on an asynchronous machine in terms of the implementation of self-excitation conditions and optimal operating modes are formulated. A simulation model of an autonomous inductive generator and a solar battery for the analysis of transient, static and dynamic modes of operation has been developed. The conducted theoretical studies of capacitive self-excitation of inductive machines have created a good basis for solving problems related to the practical use of autonomous sources based on an inductive generator.
Electrotechnical Materials
(RS Global, Warsaw, Poland, 2021) Tsyplenkov, Dmytro; Nikolenko, Anatolii; Kolb, Andrii; Grebeniuk, Andrii; Kuznetsov, Vitalii; Babyak, Mykola O.; Kovalenko, Viktor
ENG: The regularities of processes and phenomena that occur in dielectric, conductive, semiconductor and magnetic materials as part of electrical and electronic devices under the influence of energy of electric, magnetic and thermal fields are considered. The main feature of the textbook is a detailed structuring of educational material, focusing largely on the distance form of learning, as well as demonstration of the close relationship of the properties of various electrical materials and the basics of electrical engineering on specific examples. The manual is intended for students of specialties: 141 - "Electrical Energetics, Electrical Engineering and Electromechanics" and 275 - "Transport technologies", as well as for students of other specialties of higher education, which are related to the study of disciplines of electrical engineering and electronic computer science.
Enhancing Power Quality within the Context of Industrial Enterprises: Strategies for Improvement
(ScientificWorld-NetAkhatAV, Karlsruhe, Germany, 2023) Tryputen, Mykola; Kuznetsov, Vitaliy V.; Nikolenko, Anatoliy V.
ENG: The paper analyzes negative impact of poor-quality electricity on the performance of electrical installations. Particular attention is paid to the ways to improve power quality under the conditions of industrial enterprises. Use of “individual” LC-filters to protect extra important electric drives; use of “group” devices to compensate negative effect of noisy electricity at a workshop level (power active rectifiers are meant with their potential integration into the available converters for the controlled electric drives); and to inhibit voltage distortions within the areas of their origination (i.e. the mains protection against the root cause) are possible means to solve the problems.
Estimating the Probability of the Emergency Operation of the Quarry Electric Locomotive Traction Electric Drive
(RS Global Sp. z O.O., Poland, 2021) Artemenko, Artem; Chornyi, Oleksii; Sydorenko, Valeriy; Serhiienko, Serhii; Zachepa, Yurii; Kuznetsov, Vitaliy; Kuznetsova, Alisa
ENG: The paper deals with the problem of the assessment of the functionality of the multi-motor direct current traction electric drive of the quarry electric locomotive. The problem of the failure of electric drive motors because of extremely unsatisfactory state of the rail tracks and the wear of wheel pairs is analyzed. Taking into account the number of the existing repaired electric motors the probability of fitting up the traction electric drive with the electric motors with the widest electrical parameters variety is determined.
The Generalized Chaotic System in the Hyper-Complex Form and Its Transformations
(Springer, Cham, 2022) Voliansky, Roman; Volianska, Nina; Kuznetsov, Vitaliy V.; Tryputen, Mykola; Kuznetsova, Alisa; Tryputen, Maksym
ENG: The paper deals with the development of the mathematical backgrounds to design the novel chaotic systems by transforming existent ones. These backgrounds are based on using well-known shift, rotation, and scale transformations and we offer using hyper-complex numbers to simplify these transformations and represent the transformed chaotic system by using the one 1st order ordinary differential equation. In such form all well known, newly discovered and unknown chaotic systems have the similar mathematical models that are differs only by used nonlinear function of hyper complex variable in the right hand expression. That is why the consideration chaotic system dynamic in the hyper-complex domain allows us to simplify initial system definition as well without applying any transformations. This fact simplifies mathematical definition of chaotic systems and their modeling and simulation. The right-hand expression of the transformed equation in this case are defined as the combination of transformation hyper-complex numbers and source system nonlinearity which is given in the hyper-complex domain. We offer to use variable transformation factors to improve the performance of the considered chaotic system. Since the above-mentioned variable factors can be produced by other chaotic systems, we suggest designing the novel chaotic system by combining existed ones with the linear transformations. As an example, we consider the transformation of the well-known Lorenz system and show the differences between the source system and target one.
High-Performance Multiprocessor Systems
(Український державний університет науки і технологій, ННІ «Інститут промислових та бізнес технологій», 2022) Ivashchenko, Valery Petrovych; Shvachych, Gennady Grygorovych; Ivashchenko, Olena Valerievna; Sushko, Larisa Fedorovna
ENG: The paper is devoted to the modeling of high-performance multiprocessor architecture for data processing systems used to solve problems with an expandable calculations' area. The proposed system is characterized by high reliability and high energy efficiency. The system contains a separate reconfigurable network for the exchange of data between computing nodes, managed switches. The system also provides network booting nodes and redundancy mechanism of key components.
Identification of the Thermal Process in an Induction Motor
(Dnipro University of Technology, Dnipro, Ukraine, 2022) Kuznetsov, Vitalii V.; Tryputen, M.; Nikolenko, Anatolii V.; Tsyplenkov, D.; Kuvaiev, Victor; Savvin, Oleksandr V.
ENG: Purpose: synthesis of a mathematical model of an asynchronous motor, taking into account the impact of changes in the quality of electricity on the processes of heating and heat exchange for an economically justified choice of means of protection. Methodology: Theoretical substantiation of the expediency of using a one-mass thermal model of an asynchronous motor, for the conditions of operation of the latter in conditions of low-quality electricity, in order to determine losses in it. Results: Experimental studies of the operation of an asynchronous motor at nominal load were carried out. The obtained results of the measurements made it possible to determine the parameters of the single-mass thermal model, the heat transfer coefficient of the engine, and the coefficient of its heat capacity. A single-mass thermal model of an induction motor is a mathematical model used to describe the thermal processes occurring in an induction motor. This model is based on the assumption that all motor elements can be combined into one mass that heats up during engine operation. The model assumes that the thermal capacity of the motor is a constant, and the heat flow that is released during the operation of the motor is proportional to the square of the current passing through the motor windings. In addition, the model assumes the presence of thermal conductivity between the mass of the motor and the external environment, which affects the rate of heat dissipation. Scientific novelty: A methodology for determining losses in an asynchronous motor using a synthesized mathematical model is proposed, taking into account the influence of changes in the quality of electricity on the processes of heating and heat exchange in it. Practical significance: The obtained results indicate the adequacy of the proposed thermal model of an asynchronous motor operating in a network with low-quality electricity. Taking into account the fact that for many types of engines in the reference literature, there are no necessary data on the coefficients of heat transfer and heat capacity, and only the thermal time constants for certain types of engines are given, the value of the specified parameters of the model can be obtained on the basis of the methodology presented in the work. A single-mass thermal model can be useful for analyzing the thermal processes occurring in an induction motor and for improving the efficiency of the motor. In particular, it can help determine the optimal operating temperature of the motor, as well as calculate the necessary cooling system to ensure stable operation of the motor under conditions of variable load and temperature conditions.
The Impact of Connecting a Wind Power Plant on Emergency Modes of a Traction Substation of an AC Traction System
(Springer, Cham, 2022) Kachan, Yurii; Kuznetsov, Vitaliy V.; Bondar, Oleh I.
ENG: Among the countries of South-Eastern Europe, Ukraine has the greatest technical potential for the implementation of renewable energy sources, and the main part of it is wind power engineering. The traction power supply system of the railways in Ukraine can become an important transiter and consumer of electricity generated by wind power plants. At the same time, the task of ensuring traffic safety and uninterrupted power supply of traction loads requires a preliminary study of the influence of the connected wind power plant capacity on the growing short-circuit currents in the distributive units of the traction substation to which the specified connection is planned. This paper proposes a way to implement such prediction based on a systematic approach, in which a traction substation and an integrated wind power plant are considered as a single electrical-engineering complex, the sources of which work to power the short-circuit point. In previously published studies, the authors usually consider the processes in renewable energy sources and in the traction power supply system separately, without taking into account the mutual influence. The analysis of processes in the short-circuit mode is proposed to perform according to the equivalent circuits for the specified electrical-engineering complex developed by the authors with various possible options for connecting a wind power plant using mathematical modeling with proven methods of theoretical electrical engineering. The peculiarity of the study presented in this paper is also the use of the multiplication factor of the short-circuit current as a criterion for assessing the impact of the power of the connected wind power plant on the short-circuit currents of the traction substation. In our opinion, the coefficient applied by us more clearly characterizes the specified influence in comparison with operating values or complex sizes of short-circuit currents.
Improvement of Technical Service of Track Circuits
(Institute of Electrical and Electronics Engineers, IEEE, 2019) Serdiuk, Tetiana M.; Kuznetsov, Vitaliy; Serdiuk, Kseniia; Nikolenko, Anatoliy; Kuznetsova, Yevheniia; Kuznetsova, Alisa
ENG: The automated method of measuring the time and amplitude parameters of code current and parameters of track circuits (input impedance of the track circuit, a characteristic impedance, a propagation constant) were elaborated. The mathematic model of track circuits’ channel of transferring code current was improved and considered in this paper. The algorithms of definition of parameters of track circuit are offered.
Improvement of the Process of Conducting Arc-Free Ferronickel Melting in a Six-Electrode Furnace
(Elsevier/SSRN, 2021) Bezugliy, Anatolii V.; Nikolenko, Anatolii V.; Shevchenko, D. V.; Ovcharuk, Anatolii N.; Kuvaev, Viktor Iu.; Bezugliy, V. A.; Zamkovoy, O. V.
ENG: Purpose. The aim of the authors is to find a technical solution to effectively control the appearance of an arc discharge in the subelectrode space of each of the six electrodes in submerged-arc furnaces from operational point of view. Methodology. A scheme was drawn up for modeling of the furnace circuit of a six-electrode furnace, which made it possible to obtain the zero point offset voltage and control its third harmonic and other components. For this purpose, two three-phase systems were created in the electrical circuit of the six-electrode furnace, consisting of half-phases of odd and even electrodes. For each of these systems, an artificial symmetric "star" was created separately. The neutral offset voltage for each of the systems was measured between the star zero point and the conductive hearth. Findings. Analysis of the harmonic composition of the shape of the neutral offset voltage curve, created by using an artificial symmetric star, made it possible to obtain a number of information (dependencies) that can be used in control algorithms. The proposed measuring scheme was tested on operation industrial six-electrode furnace of the Pobuzhsky Ferronickel Plant. During the melting, arcs were artificially created under the electrodes. Wherein: 1) the presence of an arc discharge was confirmed by the appearance of the third harmonic of the zero point offset voltage; 2) phase shifts of the first harmonic unambiguously indicated to the electrode with an arc discharge. Practical value The proposed method for monitoring the presence of electric arcs under the electrodes can be used to control ore-thermal furnaces both independently and as an addition to the already used systems for monitoring and controlling the electric mode of six-electrode furnaces.
Improving the Reliability of Simulating the Operation of an Induction Motor in Solving the Technical and Economic Problem
(Springer, Cham, 2020) Tryputen, Mykola; Kuznetsov, Vitaliy; Kuznetsova, Alisa; Tryputen, Maksym; Kuznetsova, Yevheniia; Serdiuk, Tetiana M.
ENG: The article is devoted to the control of the statistical laws of linear voltages reproduced on a computer during computational studies on an energy-economic model when solving the problem of choosing protection tools for induction motors operating in workshop electric networks of industrial enterprises with low-quality electricity. Simultaneous and continuous estimation of average values, variances, autocorrelation and cross-correlation functions of harmonics of linear voltages is based on the adaptive approach. The article presents mathematical expressions for correcting the values of statistical quantities with the accumulation of information and proposes structural schemes for a comprehensive analysis of the results of reproduction of random variables and functions on a computer. The results of checking the values of the average values and dispersions of six harmonics of simulated linear voltages supplying an induction motor with a power of 7.5 kW are shown for the conditions of the rolling shop No. 1 of Dneprospetsstal LLC.
Integrated Use of Photovoltaic and Wind Power Plants in Power Supply Systems
(Springer, Singapore, 2022) Ostapchuk, Oleksandr; Kuznetsov, Valeriy; Bydko, Maryna; Kuznetsov, Vitaliy V.; Kuznetsova, Yevheniia
ENG: The use of energy from only one type of renewable energy source (e.g., solar and wind generation) leads to a significant increase in the cost of electricity supply due to the need to install a backup power source (energy storage system or power system). This phenomenon is caused by the significant dependence of these sources on weather conditions. The wind speed is less than 4 m/s for a long time in summer, and solar energy is not available at all in dark day periods, which in December can last up to 16 h. Accordingly, the effective use of such systems is possible only if constructing a complex application of several sources of different nature (solar and wind generation). This measure allows increasing their energy efficiency by 30–50%. The combined use of these types of distributed generation is accompanied by the equalization of the daily energy intake due to the spread of the annual maximums of energy intake, but the daily fluctuations remain pretty significant. As a result of the conducted researches, it is established that when using the share of solar energy at the level 0.4… 0.55 of the total amount, the shortest period of energy deficit (at the level of 8 days per year) is observed. At other ratios between the shares of solar and wind energy, the period of energy deficit will increase. In case of increased requirements for providing responsible consumers with electricity, it is advisable to use systems with buffer electricity storage. The developed mathematical models allow calculating the equipment parameters used in the construction of efficient power supply systems.
Investigation of the Bifurcation Properties of the Dynamics of a Biological Population Based on a Logistic Model
(Springer, Cham, 2022) Busher, Victor; Chornyi, Oleksii; Kuzenkov, Oleksandr; Tryputen, Mykola; Kuznetsov, Vitaliy V.; Rumiantsev, Vladislav
ENG: The paper substantiates the structure of the model that describes the dynamics of subpopulations in the general ecological niche. Based on the theory of bifurcations, the results of experimental studies of the effect of excess electromagnetic radiation of worn out or repaired electromechanical equipment on biological objects are analyzed. Analysis of phenotypic changes in the biological test object of Drosophila melanogaster, identified over three generations, based on the bifurcation model, made it possible to identify trends in long-term forecasts, which are in good agreement with the known results of population development in unfavorable conditions.
Lyapunov Function in the Hyper-Complex Phase Space
(Springer, Singapore, 2022) Voliansky, Roman; Volianska, Nina; Kuznetsov, Valeriy; Sadovoi, Aleksandr; Kuznetsov, Vitaliy V.; Kuznetsova, Yevheniia; Ostapchuk, Oleksandr
ENG: The paper deals with the development of background for defining Lyapunov functions for a wide range of linear dynamical objects. This background is based on assuming that the Lyapunov function is redundant energy in the considered object, and this energy is dissipated only during controlled motion. We assume the full derivative of the Lyapunov function for an autonomous motion of the control objects equals zero, and we use its summands to define linear algebraic equations. The solution of these equations allows us to find unknown terms of the Lyapunov function. The use of these terms, while the Lyapunov equation is being written down, shows that the left-hand expression in the Lyapunov equation is equal to the zero matrix. Thus, we avoid subjective assuming of quadratic form terms in the right-hand of the Lyapunov equation. We extend the proposed approach to the class dynamical system with uncertainty. This extension is performed by using interval methods, which allow defining object motions for minimal and maximal values of parameters. We show that for the control object, which parameters are not exactly known, one should consider two equations of object motions, which correspond to its trajectories on the boundaries of the intervals. Lyapunov functions are defined for these boundary trajectories. Since such an approach increases the number of the considered equations, we offer to decrease them by using hyper-complex numbers while object equations are written down.

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