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Документ Відкритий доступ Chaotic attractors in a deterministic system generator - piezoceramic transducer(UNESP – Campus de São José do Rio Preto, 2007) Krasnopolskaya, T. S.; Shvets, A. Yu.Документ Відкритий доступ Chaotic Oscillations of Nonideal Plane Pendulum Systems(CMSIM, 2012) Shvets, Aleksandr; Makaseyev, AlexanderThe atlas of maps of dynamic regimes of system ”pendulum–electric motor” is constructed. It is established that the deterministic chaos is a typical steady-state regime of the given system. Its class of Feigenbaum universality is defined. The analytical approximation of a Poincare map in a chaotic regime is discovered.Документ Відкритий доступ Complicated Scenarios of Transitions to Deterministic Chaos in Non-Ideal Dynamic Systems(NTU KhPI, 2016) Shvets, Aleksandr Yu.; Sirenko, VasiliySome of non-ideal dynamic systems are considered. It is discovered and described the complicated transition scenarios from regular to chaotic regimes and transitions between different types of chaotic regimes. Described the transition to chaos, which begins by the Feigenbaum scenario, and ends by intermittency. Also discusses the scenario of intermittency with several laminar phases and one turbulent phase. It is discovered and described transitions "hyperchaotic attractor of one type – hyperchaotic attractor of another type," which are realized according to the scenario of a generalized intermittency, but only with two rough-laminar phases.Документ Відкритий доступ Differential and Integral Equations(Igor Sikorsky Kyiv Polytechnic Institute, 2022) Kopas, Inna; Zhuravska, GannaДокумент Відкритий доступ Existence and Uniqueness of the Solution to the Cauchy Problem for the Stochastic Reaction-Diffusion Differential Equation of Neutral Type(2017) Stanzhytskii, A. N.; Tsukanova, A. O.Документ Відкритий доступ Existence and Uniqueness Results, the Markovian Property of Solution for a Neutral Delay Stochastic Reaction-Diffusion Equation in Entire Space(2019) Kenzhebaev, K. K.; Stanzhytskyi, A. N.; Tsukanova, A. O.Документ Відкритий доступ Generalized Approach for Estimating and Forecasting of Dynamical VaR and CVaR Based on Metalog Distribution(Springer, Cham, 2020) Зражевська, Віра Федорівна; Зражевський, Григорій МихайловичДокумент Відкритий доступ Higher Mathematics. Differential Equations. Practice exercises collection(КПІ ім. Ігоря Сікорського, 2022) Massalitina, E. V.; Pylypenko, V. A.Документ Відкритий доступ Higher Mathematics. Elements of Linear Algebra. Practice exercises collection(Igor Sikorsky Kyiv Polytechnic Institute, 2023) Massalitina, E. V.; Novykova, H. K.; Pylypenko, V. A.The practice book offers additional individual exercises for university students studying Elements of Linear Algebra in the course of Higher Mathematics of Igor Sikorsky KPI. The book contains 30 different variants and each variant consists of 8 exercises (16 tasks). The practice book can be recommended as an individual work on Elements of Linear Algebra for first-year students of technical specialties.Документ Відкритий доступ Higher Mathematics. Limits and Continuity. Practice exercises collection(Igor Sikorsky Kyiv Polytechnic Institute, 2023) Massalitina, E. V.; Novykova, H. K.; Pylypenko, V. A.The practice book offers additional individual exercises for university students studying Limits and Continuity in the course of Higher Mathematics of Igor Sikorsky KPI. The book contains 30 different variants and each variant consists of 9 exercises (26 tasks). The practice book can be recommended as an individual work on Limits and Continuity for first-year students of technical specialties.Документ Відкритий доступ Higher Mathematics. Quadratic Curves and Quadric Surfaces. Practice exercises collection(Igor Sikorsky Kyiv Polytechnic Institute, 2023) Pylypenko, V. A.; Massalitina, E. V.The practice book offers additional individual exercises for university students studying Quadratic Curves and Quadric Surfaces in the course of Higher Mathematics of Igor Sikorsky KPI. The book contains 30 different variants and each variant consists of 5 exercises (23 tasks). The practice book can be recommended as an individual work on Quadratic Curves and Quadric Surfaces for first-year students of technical specialties.Документ Відкритий доступ Higher Mathematics: Series: Practice Book(Igor Sikorsky KPI, 2022) Massalitina, E. V.; Pylypenko, V. A.Документ Відкритий доступ Hyperchaos in Oscillating Systems with Limited Excitation(Springer, Cham, 2019) Shvets, Aleksandr; Sirenko, VasiliyThe oscillating systems of a pendulum type, nonideal in the sense of Sommerfeld-Kononenko are considered. Such systems are used for modeling oscillations in hydrodynamics, shell theory and other applications. The complex scenario of transition to the hyperchaos is revealed and described in details. Revealed scenario begins with symmetric limit cycles and ends with a transition to hyperchaos through generalized intermittency with two coarse grained laminar phases. This scenario is illustrated in detail by projections of phase portraits, Poincaré sections and other characteristics of attractors of the system.Документ Відкритий доступ Modeling of Finite Inhomogeneities by Discret Singularities(Київський національний університет імені Тараса Шевченка, 2021) Зражевська, Віра Федорівна; Зражевський, Григорій МихайловичДокумент Відкритий доступ Modeling of the influence of delay factors on the dynamics of non-ideal pendulum systems(Київський національний університет імені Тараса Шевченка, МП "ТВ і МС", 2015) Makaseyev, A. M.; Shvets, A. Yu.The influence of various factors of delay on the dynamics of non-ideal dynamical systems “pendulum-electric motor” is considered. The approaches that allow to reduce the mathematical model of the system to the systems of differential equations without delay are proposed. The maps of dynamical regimes, the dependencies of maximal non-zero Lyapunov’s characteristic exponent and phase- parametric characteristics of these systems are studied. The scenarios of transition from steady-state regular regimes to chaotic ones are identified.Документ Відкритий доступ On Comparison Results for Neutral Stochastic Differential Equations of Reaction-Diffusion Type in L_{2}(ℝ^{d})(Springer Nature Switzerland AG, 2019) Stanzhytskyi, Oleksandr M.; Mogilova, Viktoria V.; Tsukanova, Alisa O.Документ Відкритий доступ Peculiarities of Transition to Chaos in Nonideal Hydrodynamics Systems(CMSIM, 2012) Shvets, Aleksandr; Sirenko, VasiliyThe nonideal deterministic dynamic system ”tank with a fluid–electromotor” is considered. On the basis of investigation of low-dimensional mathematical model of the given system the map of dynamic regimes is constructed. The study of scenarios of transition to deterministic chaos is carried out. Atypical peculiarities of realization of such scenarios are described.Документ Відкритий доступ QUINTILE REGRESSION BASED APPROACH FOR DYNAMICAL VAR AND CVAR FORECASTING USING METALOG DISTRIBUTION(КПІ ім. Ігоря Сікорського, 2021) Зражевська, Віра Федорівна; Зражевський, Григорій МихайловичДокумент Відкритий доступ Theory of Series Elements of Theory of Functions of a Complex Variable Operational Calculus(Igor Sikorsky Kyiv Polytechnic Institute, 2024) Karpaluk, Tamara; Kopas, Inna; Reva, Nadia; Zhuravska, GannaThis textbook is designed for students of the Specialty 131 "Applied Mechanics", studying the discipline "Higher Mathematics 3. Series. Theory of the Functions of a Complex Variable" in English. The textbook introduces the concepts of numerical, functional, power and Fourier series; application of series; the theory of the functions of a complex variable, including differentiation and integration technics, Laurent series, the residue theory and its applications; the basic concepts of the Laplace and Fourier transforms and their applications. Each part contains basic mathematical conceptions, explains new mathematical terms and is provided review questions and exercises, which will allow students to master the skills of solving practical problems. The most important concepts of the theory are explained and illustrated by figures and examples to help clarify the theory and show some applications. The textbook can be also recommended to students of other specialties, who study Theory of Series and Theory of the Functions of a Complex Variable. The manual can be used to provide full-time, distance or mixed education.Документ Відкритий доступ Біфуркації аттракторів динамічних систем. Робоча програма навчальної дисципліни (Силабус)(КПІ ім. Ігоря Сікорського, 2022) Швець, Олександр Юрійович