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The Control of Chaos: Methods and Applications
Hůlka, Tomáš ; Dvořák, Jiří (referee) ; Matoušek, Radomil (advisor)
This thesis focuses on deterministic chaos and selected methods of chaos control. It briefly describes the matter of deterministic chaos and presents commonly used tools of analysis of dynamical systems exhibiting chaotic behavior. A list of frequently studied chaotic systems is presented and followed by a description of methods of chaos control and the optimization of these methods. The practical part is dedicated to the stabilization of two model systems and one real system with described methods.
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Analýza atraktorů zobecněných Newtonovských tekutin v 3d oblastech
Žabenský, Josef ; Pražák, Dalibor (advisor) ; Bulíček, Miroslav (referee)
We investigate a system of nonlinear partial differential equations, specifically the so-called Ladyzhenskaya model, in three spatial dimensions. It will be shown that after inclusion of a perturbation of a higher order, the model exhibits a considerably better behavior, in particular it will become quite straightforward to prove differentiability of solutions with respect to the initial condition. Due to this fact we may consequently employ the method of Lyapunov exponents to estimate the fractal dimension of the exponential attractor. First, however, it will be necessary to show existence and uniqueness of solutions, improved regularity and existence of a compact invariant set for the entire system.
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Automatic Photo Sorting
Weiser, Michal ; Španěl, Michal (referee) ; Beran, Vítězslav (advisor)
The purpose of this article is to show how intuitive can be work with pictures sorting. Drag&drop technology in combination with interactive picture moving makes this application easy to use. To sort pictures with some feature you just must drag magnetic attractor into some place in workspace and choose attracting feature with specific value. Pictures with alike value are attracted. Difference in values determines the distance between picture and attractor. Combination of many attractors can help you sort pictures in short time with just couple of clicks.
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Fractals in Computer Graphics
Heiník, Jan ; Španěl, Michal (referee) ; Herout, Adam (advisor)
This Master's thesis deals with history of Fractal geometry and describes the fractal science development. In the begining there are essential Fractal science terms explained. Then description of fractal types and typical or most known examples of them are mentioned. Fractal knowledge application besides computer graphics area is discussed. Thesis informs about fractal geometry practical usage. Few present software packages or more programs which can be used for making fractal pictures are described in this work. Some of theirs capabilities are described. Thesis' practical part consists of slides, demonstrational program and poster. Electronical slides represents brief scheme usable for fractal geometry realm lectures. Program generates selected fractal types. Thesis results are projected on poster.
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Algorithms for computation of the dimensions of state space attractors
Götthans, Tomáš ; Slanina, Martin (referee) ; Petržela, Jiří (advisor)
The geometry of chaotic attractors can be complex and difficult to describe without some mathematical tool. The topic of this contribution is the realization of program for computing the dimensions of state space attractors. We can also find out if the system is highly sensitive to initial conditions. First we need to numerically integrate system of equations, create a data set and finally we can estimate the capacity or Kaplan-Yorke dimension. The main objective of derived program is to analyze and determine chaotic behavior providing a chance to discuss the accuracy of computation engine and theoretical value.
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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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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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