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Periodic problem for the Duffing equation
Asante, Michael Onwona ; Řehák, Pavel (referee) ; Šremr, Jiří (advisor)
Při matematickém modelování fyzikálních systémů se používají obyčejné diferenciální rovnice různých tvarů. Diferenciální rovnice popisující tyto systémy jsou často složité nelineární rovnice, avšak pomocí vhodných aproximací nelinearity lze odvodit jednoduché rovnice zvané Duffingovy rovnice, které lze analyticky studovat. V matematickém modelování mechaniky problém hledání periodických řešení těchto Duffingových rovnic úzce souvisí s existencí periodických vibrací jeho odpovídajícího nelineárního oscilátoru. V této práci je provedena analýza řešení a existence řešení v autonomních a neautonomních případech uvažované Duffingovy rovnice s podporou simulací v MATLAB.
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Automatic Computation Control
Opálka, Jan ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work deals with the automatic control of numerical calculations. The reader is acquainted with the numerical solution of differential equations and the parallel, serial, and series-parallel numerical integrator. The practical aim of this work is to design control circuits for the three mentioned variants of integrators. The design includes the development of a software simulator of the control circuit for the series-parallel integrator in a fixed point.
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Frequency Responses
Urbánek, Radim ; Kraus, Michal (referee) ; Kunovský, Jiří (advisor)
The aim of this MSc Thesis is to create a system for automatic generation of frequency characteristics of electrical circuits. These circuits are described by differential equations. A special simulator of RLC circuit has been created and frequence response, vector diagram can be generated. This system has been mainly suggested for application in education. The process of solving differential equations is based on the Taylor method. Systems in general is the theoretical part of this project. Different definitions of systems their divission ,basic phenomenons and mathematical devices are described there. Next chapter deals with the mathematical devices for solving differential equations which makes the basis for description of phenomenons in these systems. There are also systems TKSL and TKSL/C. In the next chapter I was investigaty the analyze of vector diagrams for simple and more difficult circuits. I have found a solution for actual circuit by this technique. The last chapter is devoted to the frequency characteristics and descriptions of simulation program for generation the frequency characteristics.
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Pursuit problems: basic models and their analysis
Neugebauer, Tomáš ; Řehák, Pavel (referee) ; Čermák, Jan (advisor)
This thesis is focused on creation of mathematical models and analysis of basic pursuit problems. In particular, the Perrault's problem, the Bouguer's problem, the Hathaway’s problem, the snail–racehorse problem and the Bailey's problem are involved. Each of the problems is solved analytically or numerically, including qualitative analysis.
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Simulation of electrophysiological experiments
Kubáček, Svatopluk ; Provazník, Ivo (referee) ; Rychtárik, Milan (advisor)
Simulation of electrophysiological experiments enables to gain valuable data about bioelectrical processes occurring on isolated cells. This thesis deals with basic principals allowing the creation of bioelectrical phenomenons and measuring techniques that need to be used in order to collect information about these phenomenons. The outcome of the thesis is a programme that serves as an instrument for simulation of measuring techniques applied on Luo-Rudy model. The programme contains basic measuring techniques – current clamp and voltage clamp – providing the possibility to change basic parameters of the model. The results of this work are later compared with the accessible literature.
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Electric Circuits Simulations in a Specialized Parallel System
Janko, Roman ; Šátek, Václav (referee) ; Kunovský, Jiří (advisor)
This work provides an overview of methods for the numerical solution of differential equations. Options of their parallelization, a division of computational operations on multiple microprocessors, are provided with emphasis placed on the Taylor series. The next part of the work is devoted to the description of a specialized parallel system, which was design to fast solving of these equations. Differential equations are appropriate to describe electrical circuits. An important characteristic of each circuit is its behavior in the frequency domain. The aim of this thesis was to design and implement a program which investigate frequency characteristics of AC circuits. A method for analyzing a circuit and automatically assembling corresponding equations is presented. These differential equations are then solved in TKSL. At the end of this work a time consumption is evaluated and compared with Matlab.
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Linear Matrix Differential Equation with Delay
Piddubna, Ganna Konstantinivna ; Růžičková, Miroslava (referee) ; Dzhalladova, Irada (referee) ; Baštinec, Jaromír (advisor)
V předložené práci se zabýváme hledáním řešení lineární diferenciální maticové rovnice se zpožděním x'(t)=A0x(t)+A1x(t-tau), kde A0, A1 jsou konstantní matice, tau>0 je konstantní zpoždění. Dále se zabýváme odvozením podmínek stability řešení systému a řiditelnosti daného systému. Pro řešení tohoto systému byla použita metoda "krok za krokem". Řešení bylo nalezeno jak v rekurentní formě tak i v obecném tvaru. Je provedena analýza stability a asymptotické stability řešení systému. Jsou zformulovány podmínky stability. Hlavní roli v analýze stability měla metoda Lyapunovových funkcionálů. Jsou zformulovány nutné a postačující podmínky řiditelnosti pro případ systémů se stejnými maticemi a je zkonstruována řídící funkce. Jsou odvozeny postačující podmínky pro řiditelnost v případě komutujících matic a v případě obecných matic a je sestrojena řídící funkce. Všechny výsledky jsou ilustrovány na netriviálních příkladech.
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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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