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In dust we trust
Rujbr, Kamil ; Opekar), Ondřej (referee) ; Rathouský, Luděk (advisor)
Through the papers and canvas I tell the story of everyday addiction that surrounds us. I start from my personal feelings and suck the atmosphere of the city and places from the edge of society. This theme is presented in the form of abstract drawings and paintings, in which certain phases and processes are displayed. I capture chaos in new forms so that the image, even within the technologically advanced and in all directions of the expanding visual culture, does not lose the liveliness, sense and critical justification for its further existence. The paintings and drawings are a visit to the world of people who are not the majority of the world and are all in a way lonely and lonely in their own way.
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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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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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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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Methods of indicating chaos in nonlinear dynamical systems
Tancjurová, Jana ; Šremr, Jiří (referee) ; Nechvátal, Luděk (advisor)
The master's thesis deals mainly with continuous nonlinear dynamical systems that exhibit chaotic behavior. The main goal is to create algorithms for chaos detection and their subsequent testing on known models. Most of the thesis is devoted to the estimation of the Lyapunov exponents, further it deals with the estimation of the fractal dimension of an attractor and summarizes the 0--1 test. The thesis includes three algorithms created in MATLAB -- an algorithm for estimating the largest Lyapunov exponent and two algorithms for estimating the entire Lyapunov spectra. These algorithms are then tested on five continuous dynamical systems. Especially the error of estimation, speed of these algorithms and properties of Lyapunov exponents in different areas of system behavior are investigated.
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Can extended bodies follow geodesic trajectories?
Lukes-Gerakopoulos, Georgios ; Mukherjee, Sajal
We provide an extension of the analysis on whether an extended test body can follow a geodesic trajectory given by Mukherjee et al. (2022). In particular, we consider a test body in a pole-dipole-quadrupole approximation under the Ohashi-Kyrian-Semer´ak spin supplementary condition moving in the Schwarzschild and Kerr background. Using orbital setups under which a pole-dipole body can follow geodesic motion, we explore under which conditions this can also take place in the pole-dipole-quadrupole approximation when only the mass quadrupole is taken into account. For our analysis, we employ the assumption that the dipole contribution and the quadrupole contribution vanish independentlly.
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Growth of orbital resonances around a black hole surrounded by matter
Stratený, Michal ; Lukes-Gerakopoulos, Georgios
This work studies the dynamics of geodesic motion within a curved spacetime around a Schwarzschild black hole, perturbed by a gravitational field of a far axisymmetric distribution of mass enclosing the system. This spacetime can serve as a versatile model for a diverse range of astrophysical scenarios and, in particular, for extreme mass ratio inspirals as in our work. We show that the system is non-integrable by employing Poincaré surface of section and rotation numbers. By utilising the rotation numbers, the widths of resonances are calculated, which are then used in establishing the relation between the underlying perturbation parameter driving the system from integrability and the quadrupole parameter characterising the perturbed metric. This relation allows us to estimate the phase shift caused by the resonance during an inspiral.
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Analysis of chaotic behavior in double pendulum
Brázda, Tomáš ; Lošák, Petr (referee) ; Sosna, Petr (advisor)
This thesis deals with the presentation of basic knowledge regarding chaos theory. There are mentioned several basic methods of dimension calculation as well as the overall use of this theory in various scientific disciplines. The main part is devoted to the complete analysis of a double pendulum. To initiate into the issue, this situation was outlined on a simple mathematical basis pendulum. There is derived a numeral system of two differential equations of second order to work with the double pendulum. Thanks to computer program Matlab there was created a fractal that represents chaotic behavior of the double pendulum. Knowledge acquired from dimension calculation was used here to classify the fractal and to work out its dimension. In addition there was analyzed impact of parameters of behavior in system. This overall chaotic behavior has been verified by the largest Lyapunov exponent and the 0–1 test, which identified areas, where this system behaves chaotically and where it is stable.
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