Кафедра математичної фізики та диференціальних рівнянь (КМФДР)

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    Chaotic attractors in a deterministic system generator - piezoceramic transducer
    (UNESP – Campus de São José do Rio Preto, 2007) Krasnopolskaya, T. S.; Shvets, A. Yu.
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    Chaotic Oscillations of Nonideal Plane Pendulum Systems
    (CMSIM, 2012) Shvets, Aleksandr; Makaseyev, Alexander
    The 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.
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    Complicated Scenarios of Transitions to Deterministic Chaos in Non-Ideal Dynamic Systems
    (NTU KhPI, 2016) Shvets, Aleksandr Yu.; Sirenko, Vasiliy
    Some 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.
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    Differential and Integral Equations
    (Igor Sikorsky Kyiv Polytechnic Institute, 2022) Kopas, Inna; Zhuravska, Ganna
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    Generalized Approach for Estimating and Forecasting of Dynamical VaR and CVaR Based on Metalog Distribution
    (Springer, Cham, 2020) Зражевська, Віра Федорівна; Зражевський, Григорій Михайлович
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    Higher Mathematics. Differential Equations. Practice exercises collection
    (КПІ ім. Ігоря Сікорського, 2022) Massalitina, E. V.; Pylypenko, V. A.
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    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.
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    Higher Mathematics. Indefinite Integral
    (Igor Sikorsky Kyiv Polytechnic Institute, 2025) Massalitina, Уevgeniia; Pylypenko, Vita
    Practicum offers additional individual exercises for university students studying Indefinite Integral in the course of Higher Mathematics of Igor Sikorsky Kyiv Polytechnic Institute. The study aid contains 31 different variants and each variant consists of 36 tasks. Students master the material being studied and consolidate the acquired knowledge by solving such individual tasks. The practicum can be recommended as an individual work on Indefinite Integral for the first-year students of technical specialties.
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    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.
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    Higher Mathematics. Operational Calculus
    (Igor Sikorsky Kyiv Polytechnic Institute, 2025) Massalitina, Уevgeniia; Pylypenko, Vita
    Practicum offers additional individual exercises for university students studying Operational Calculus in the course of Higher Mathematics of Igor Sikorsky Kyiv Polytechnic Institute. The study aid contains 30 different variants and each variant consists of 5 exercises (11 tasks). Students master the material being studied and consolidate the acquired knowledge by solving such individual tasks. The practicum can be recommended as an individual work on Operational Calculus for the second-year students of technical specialties.
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    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.
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    Higher Mathematics: Series: Practice Book
    (Igor Sikorsky KPI, 2022) Massalitina, E. V.; Pylypenko, V. A.
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    Hyperchaos in Oscillating Systems with Limited Excitation
    (Springer, Cham, 2019) Shvets, Aleksandr; Sirenko, Vasiliy
    The 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.
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    Modeling of Finite Inhomogeneities by Discret Singularities
    (Київський національний університет імені Тараса Шевченка, 2021) Зражевська, Віра Федорівна; Зражевський, Григорій Михайлович
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    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.
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    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.
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    Peculiarities of Transition to Chaos in Nonideal Hydrodynamics Systems
    (CMSIM, 2012) Shvets, Aleksandr; Sirenko, Vasiliy
    The 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.
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    QUINTILE REGRESSION BASED APPROACH FOR DYNAMICAL VAR AND CVAR FORECASTING USING METALOG DISTRIBUTION
    (КПІ ім. Ігоря Сікорського, 2021) Зражевська, Віра Федорівна; Зражевський, Григорій Михайлович