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Fractional decision making models in networks
Malárik, Peter ; Nechvátal, Luděk (referee) ; Kisela, Tomáš (advisor)
This thesis deals with the problem of modelling specific types of complex systems using networks, especially those that indicate the possible occurrence of so-called fractional dynamics. Two variants of the Voter Model, which is one of the basic decision models describing the propagation of opinions in a social setting, are presented. By enriching the dynamics of the model with history dependence and by setting the system over different kinds of networks, we observe qualitative changes in behavior that are typical in the presence of the aforementioned fractional dynamics. We look at this issue from the point of view of numerous model simulations, which results are graphically presented, discussed and compared with known theory.
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Circuit realizations of special chaotic dynamical systems
Kaleta, Lukáš ; Langhammer, Lukáš (referee) ; Petržela, Jiří (advisor)
This thesis deals with the circuit synthesis of two given chaotic dynamic systems. The introduction of the work analyses a theory of dynamic systems, a theory of chaos and methods of chaotic circuits synthesis. The practical part contains a derivation of circuits from specified systems of differential equations with an integrator synthesis method and polynomial expansion of resonant circuit equations. Following realization of the circuits is included. The output of the work are the results of numerical integrations of specified systems, simulations of synthesized circuits and measurements on implemented circuits. Results are in a form of state portraits and frequency spectra, ilustrating the induced chaotic phenomena.
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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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Unconventional Signals Oscillators
Hruboš, Zdeněk ; Galajda, Pavol (referee) ; Štork, Milan (referee) ; Petržela, Jiří (advisor)
Dizertační práce se zabývá elektronicky nastavitelnými oscilátory, studiem nelineárních vlastností spojených s použitými aktivními prvky a posouzením možnosti vzniku chaotického signálu v harmonických oscilátorech. Jednotlivé příklady vzniku podivných atraktorů jsou detailně diskutovány. V doktorské práci je dále prezentováno modelování reálných fyzikálních a biologických systémů vykazujících chaotické chování pomocí analogových elektronických obvodů a moderních aktivních prvků (OTA, MO-OTA, CCII ±, DVCC ±, atd.), včetně experimentálního ověření navržených struktur. Další část práce se zabývá možnostmi v oblasti analogově – digitální syntézy nelineárních dynamických systémů, studiem změny matematických modelů a odpovídajícím řešením. Na závěr je uvedena analýza vlivu a dopadu parazitních vlastností aktivních prvků z hlediska kvalitativních změn v globálním dynamickém chování jednotlivých systémů s možností zániku chaosu v důsledku parazitních vlastností použitých aktivních prvků.
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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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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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Analysis and circuit realization of special chaotic systems
Rujzl, Miroslav ; Hruboš, Zdeněk (referee) ; Petržela, Jiří (advisor)
This master‘s thesis deals with analysis of electronic dynamical systems exhibiting chaotic solution. In introduction, some basic concepts for better understanding of dynamical systems are explained. After introduction, current knowledge from the world of circuits exhibiting chaotic solutions are discussed. The best-known chaotic systems are analyzed numerically in Matlab software. Numerical analysis and experimental verification were demonstrated at C class transistor amplifier, which confirmed the chaotic behavior and generation of a strange attractor.
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Chimney demolition modeling
Ficker, Tomáš ; Keršner, Zbyněk (referee) ; Frantík, Petr (advisor)
The thesis deals with solving of a discrete dynamic 2D model of a chimney during its demolition. Specific goal of the thesis is to clarify observed phenomenon that is a break of the chimney while falling. The model of the chimney is designed and solved using software FyDiK which is able to solve dynamic effects. For verification of results, two models of chimney have been designed.
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