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Chaos
Vogelová, Tereza ; Fajnor, Richard (referee) ; Stratil, Václav (advisor)
The existing world is becoming more disrupted and is falling apart. For its resurrection and restoration, a new way of thinking is necessary. This new type of thinking is needed to be able to open up its mind and to think about the process of thinking itself; it must understand what is happening in other systems, where processes seem to be taking place by themselves without any other visible interference. First Chaos is the title for an intermedia installation which contains 90 black and white photographs, both digital and analogue, all of which were taken between the years 2008 and 2012. Together, the photographs create one coherent piece – a kind of sculpture. They can evoke a "still film" with a non-linear, cyclical storyline, whilst the images can simultaneously function individually, without any connection to other photographs.
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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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Constructing Artificial Chaos
Hakl, Vilém ; VAJCHR, Marek (advisor) ; ŠERÝ, Ladislav (referee)
This work is about works of art which imitate chaos in terms of their structure. The focus of this work is POETICS OF CHAOS, in other words: specific techniques used to construct artificial chaos. The poetics of chaos is also explored through narration, the grotesque anti-myth about Eris, the Goddess of Chaos, and Paris, the prince of Troy, and his horrifying masturbation phantasy. The main field of this work is literature and film, but music and painting are also explored. The analysis of SPAS (a novel by Ivan Matousek) and ASTHENIC SYNDROME (a film by Kira Muratova) are included, because the structure of these masterpieces is brilliantly chaotic.
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Nonlinear Physics and Chaos Theory
NÁHLÍK, Tomáš
This thesis deals with nonlinear physics and chaos theory from its begining, through the main people to its application in various fields. This work has also part of fractals and fractal geometry. There are also source codes of various examples.
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Experimental research chaos and his visualization
Kratochvíl, Ctirad ; Koláčný, J. ; Houfek, Lubomír ; Houfek, Martin ; Švéda, P.
Theory chaos like of science discipline unreel approximately from halves sixtieth years last century. Most washing is but till this time devoted theoretic aspects hereof prodigy and their investigation pursues as a rule on modelling systems with small number degree of freedom - concerning technical application. In his benefit put to record simulator studies chaotic phenomenon, which were gained with utilization, chaos modulus on mock - ups nonlinear dynamic systems. K visualization achieved results then use memory oscilloscope.
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Chaotické kmitání rázové soustavy s měkkým zdrojem energie
Půst, Ladislav
Influence of weak source of exciting on the vibrations of mechanical system with elastic stop is investigated. Level of hard energy source changes damping of oscillating system and influences origine of quasi periodic and chaotic oscillations. Weak source of excitation increases of motion and suppresses dangerous chaotic motions.
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Robustnost testu iid založeného na principu korelačního integrálu
Briatka, Ľuboš
Kočenda (2001) introduced the test for nonlinear dependencies in time series data based on the correlation integral. The idea of the test is to estimate the correlation dimension by integrating over a range of proximity parameter. However, there is an unexplored avenue if one wants to use the test to identify nonlinear structure in non-normal data. Using Monte Carlo studies we show that non-normality leads to over-rejection of the null hypothesis due to two reasons: first, the data are not iid; and second, the data are nonnormal. It is shown that even very small deviation from normality could lead to a rejection of the null hypothesis and hence wrong conclusion. The bootstrap method is revisited and it is shown that it helps to avoid the over-rejection problem, moreover the power of the test increases by a significant amount.
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