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Delay Differential Equations in Dynamic Systems
Dokyi, Martha ; Šremr, Jiří (referee) ; Opluštil, Zdeněk (advisor)
Tato práce je přehledem zpožděných diferenciálních rovnic v dynamických systémech. Počínaje obecným přehledem zpožděných diferenciálních rovnic představujeme koncept zpožděných diferenciálů a použití jeho modelů, od biologie a populační dynamiky po fyziku a inženýrství. Poskytneme také přehled Dynamické systémy a diferenciální rovnice zpoždění v dynamických systémech. Oblastí pro modelování s rovnicemi zpožďovacích diferenciálů je Epidemiologie. Důraz je kladen na vývoj epidemiologického modelu Susceptible-Infected-Removed (SIR) bez časového zpoždění. Analyzujeme naše dva modely v rovnováze a lokální stabilitě pomocí předpokládaných dat COVID -19. Výsledky by byly porovnány mezi modelem bez zpoždění a modelem se zpožděním.
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Universal and fully analog oscillator with transconductance amplifiers
Kus, Václav ; Zaplatílek, Karel (referee) ; Hruboš, Zdeněk (advisor)
The aim of this thesis is to design a universal analog oscillator using transconductance amplifiers. For studying behaviour of chaotic dynamical systems can be used systems Class C. Suitable way for the purpose modeling dynamic phenomena arising in these systems is an electronic circuit that exhibits the same behavior as modeled system. After familiarization with the basic principles of synthesis of integrators systems, and studying the involvement of frequently used functional blocks were designed the concept of universal chaotic oscillator using transconductance amplifiers. The functionality of this circuit has been verified by PSpice simulation program. A typical feature of chaotic oscillator is extremely sensitivity to initial conditions. Each small change on the initial parameters can lead to major change in the shape of the attractor. The result of this thesis is a functional sample of a universal chaotic oscillator, which was verified by the dynamic behavior of the given differential equations.
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Stability and control of dynamical systems used in modeling an airplane motion
Novák, Jiří ; Šremr, Jiří (referee) ; Nechvátal, Luděk (advisor)
A modern aircraft (or another machine moving in the air) usually does not rely on its structural stability only. In fact, the motion is conventionally stabilized using a loop feedback control. A dynamical system, which models the aircraft's position and orientation in time, reacts on the state variables, hence, the control signal is dynamically changed. This bachelor's thesis deals with deriving the equations of motion for small perturbations of the state variables as well as with stability and control of such a system of equations. In addition, comparison of both a nonlinear and a linearized model is a part of this work. The programming language Python is used for testing on several examples of a concrete aircraft.
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Fractals in Computer Graphics
Šelepa, Jan ; Venera, Jiří (referee) ; Sumec, Stanislav (advisor)
The goal of this work is to give introduction and specification of fractals. The first chapter presents the basics of fractal geometry. The second chapter maps the history of fractals and points out the most important people of fractal science. The third chapter presents fractal classification based on several criteria and gives basic examples. The fourth chapter is a summary of widely used applications for fractal creation. The last chapter describes the application that was made to demonstrate given algorithms and fractals mentioned in this thesis.
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Visual Educational System of Fractals
Friedrich, Tomáš ; Škarvada, Jaroslav (referee) ; Gajda, Zbyšek (advisor)
The target of this work is to explain basics of fractals generation and theory. The introdaction to the fractal geometry is mentioned first. Certain types od fractals are explained and demostrated by examples next.For easier understanding of all mentioned types of fractals a grafical aplication was designed where it is possible to experience fractals characteristics and behaviour. The aplication is available on the internet.
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Equivalent circuit realizations of the simple chaotic oscillators
Kobza, Jaromír ; Dostál, Tomáš (referee) ; Petržela, Jiří (advisor)
The aim of this paper is to introduce with basic theory the problems encountered when considering the circuit implementation of autonomous RC chaotic oscillator with nonlinearity. All oscillator prototypes are based on one type of universal oscillator circuit. This circuit is able to generate a lot of attractors on condition of different entrance parameters. The design is based on a mathematical simulation, which includes the generation of electronic circuit values. The work is focused the transformation of these values to operational circuit configuration and simulation in a circuit simulator. The final task is to acquire chaotic attractors. Oscilloscope and spectrum analyser photos will verify the operation.
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Physical and Mathematical modelling of Chimney Demolition
Ficker, Tomáš ; Keršner, Zbyněk (referee) ; Frantík, Petr (advisor)
The thesis deals with physical and numerical modelling of downsized model of chimney and its demolition. The properties of downsized physical model, which is made of wooden cubes, are being researched and experimentally tested. The physical experiments are then designed using software FyDiK. Numerical Model is simplified to 2D problem, whereas the problem includes dynamic effects. Conformity of designed software model and physical experiment is tested. The aim of this thesis is to achive the best possible conformity of physical and numerical models.
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Periodic boundary value problem in mathematical models of nonlinear oscillators
Kyjovský, Adam ; Nechvátal, Luděk (referee) ; Šremr, Jiří (advisor)
This master's thesis deals with qualitative analysis of nonlinear differential equations of second order. For autonomous equations some basic notions of Hamiltonian systems (mainly construction of phase portrait) are presented. For non-autonomous equations the method of lower and upper functions for periodic boundary value problem is used. These notions are then applied to a model of mechanical oscillator, a question of existence of solutions to autonomous and non-autonomous nonlinear differential equations is studied.
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