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Methods for electroencephalogram records comparison
Kliment, Juraj ; Ronzhina, Marina (referee) ; Janoušek, Oto (advisor)
The bachelor thesis deals with the comparison of EEG signals from the human brain. The aim of this work is to find suitable nonlinear parameters, based on which it is possible to compare EEG records created in different conditions. The selected parameters are then tested on data from a publicly available database using Matlab software, the results are statistically processed and compared with the results of existing scientific studies. The comparison was based on the parameters Approximate entropy, Correlation dimension, Hurst exponent and Lyapunov exponent.
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Analysis of Logistic Maps
Adeleke, Joshua Owolabi ; Šremr, Jiří (referee) ; Řehák, Pavel (advisor)
Logistická mapa souvisí s diskrétní logistickou rovnicí. Na rozdíl od svého kontinuálního protějšku vykazuje logistická diferenční rovnice velmi komplikovanou dynamiku včetně chaotiky chování. Tato práce tak zkoumala kvalitativní chování logistické mapy podle pomocí některých matematických nástrojů. Tato dynamika byla studována systematicky, a to tak, aby její povaha byla čistá forma až do bodu, kdy bylo komplikované se s ní vypořádat, byly pečlivě studovány. dále pojem konjugace byl zaměstnán v okamžiku, kdy jeho analytický výpočet představoval být komplikovaný, s čímž byly dále odhaleny jeho vlastnosti. Byly učiněny pozoruhodné závěry, mezi nimiž je popis chaotického chování logistická mapa, jak ji odhaluje její spojení se stanovou mapou. V průběhu této studie tedy existuje další nástroj pro vyšetřování chaotického chování byla poznamenána logistická mapa, která je symbolickou dynamikou, se kterou se bude v budoucnu studovat logistická mapa může zabrat.
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Methods for electroencephalogram records comparison
Kliment, Juraj ; Ronzhina, Marina (referee) ; Janoušek, Oto (advisor)
The bachelor thesis deals with the comparison of EEG signals from the human brain. The aim of this work is to find suitable nonlinear parameters, based on which it is possible to compare EEG records created in different conditions. The selected parameters are then tested on data from a publicly available database using Matlab software, the results are statistically processed and compared with the results of existing scientific studies. The comparison was based on the parameters Approximate entropy, Correlation dimension, Hurst exponent and Lyapunov exponent.
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Bifurcations in a chaotic dynamical system
Kateregga, George William ; Tomášek, Petr (referee) ; Nechvátal, Luděk (advisor)
Dynamical systems possess an interesting and complex behaviour that have attracted a number of researchers across different fields, such as Biology, Economics and most importantly in Engineering. The complex and unpredictability of nonlinear customary behaviour or the chaotic behaviour, makes it strange to analyse them. This thesis presents the analysis of the system of nonlinear differential equations of the so--called Lu--Chen--Cheng system. The system has similar dynamical behaviour with the famous Lorenz system. The nature of equilibrium points and stability of the system is presented in the thesis. Examples of chaotic dynamical systems are presented in the theory. The thesis shows the dynamical structure of the Lu--Chen--Cheng system depending on the particular values of the system parameters and routes to chaos. This is done by both the qualitative and numerical techniques. The bifurcation diagrams of the Lu--Chen--Cheng system that indicate limit cycles and chaos as one parameter is varied are shown with the help of the largest Lyapunov exponent, which also confirms chaos in the system. It is found out that most of the system's equilibria are unstable especially for positive values of the parameters $a, b$. It is observed that the system is highly sensitive to initial conditions. This study is very important because, it supports the previous findings on chaotic behaviours of different dynamical systems.
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Analysis and Prediction of Foreign Exchange Markets by Chaotic Attractors and Neural Networks
Pekárek, Jan ; Dostál, Petr (referee) ; Budík, Jan (advisor)
This thesis deals with a complex analysis and prediction of foreign exchange markets. It uses advanced artificial intelligence methods, namely neural networks and chaos theory. It introduces unconventional approaches and methods of each of these areas, compares them and uses on a real problem. The core of this thesis is a comparison of several prediction models based on completely different principles and underlying theories. The outcome is then a selection of the most appropriate prediction model called NAR + H. The model is evaluated according to several criteria, the pros and cons are discussed and approximate expected profitability and risk are calculated. All analytical, prediction and partial algorithms are implemented in Matlab development environment and form a unified library of all used functions and scripts. It also may be considered as a secondary main outcome of the thesis.
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Automatic Analysis of Heart Rate Variability Signals
Kubičková, Alena ; Halámek, Josef (referee) ; Lhotská, Lenka (referee) ; Kozumplík, Jiří (advisor)
This dissertation thesis is dedicated to the heart rate variability and methods of its evaluation. It mainly focuses on nonlinear methods and especially on the Poincaré plot. First it deals with the principle and nature of the heart rate variability, then the ways of its representation, linear and also nonlinear methods of its analysis and physiological and pathophysiological influence on heart rate variability changes. In particular, there is emphasis on the metabolic syndrome. In the next section of the thesis there are compared and evaluated different ways of representation of the heart rate variability and further are tested selected methods of heart rate variability analysis on unique data from patients with the metabolic syndrome and healthy subjects provided by the Institute of Scientific Instruments, Academy of Sciences of Czech Republic. In particular, they are used the Poincaré plot and its parameters SD1 and SD2, commonly used time domain and frequency domain parameters, parameters evaluating signal entropy and the Lyapunov exponent. SD1 and SD2 combining the advantages of time and frequency domain methods of heart rate variability analysis distinguish successfully between patients with the metabolic syndrome and healthy subjects.
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Similarities in chaotic behavior of Lorenz 05 model and ECMWF models
Bednář, Hynek ; Raidl, Aleš (advisor) ; Jaňour, Zbyněk (referee) ; Pokorný, Pavel (referee)
This thesis tests the ability of the Lorenz's (2005) chaotic model to simulate predictability curve of the ECMWF model calculated from data over the 1986 to 2011 period and demonstrates similarity of the predictability curves for the Lorenz's model with N = 90 variables. This thesis also tests approximations of predictability curves and their differentials, aiming to correct the ECMWF model estimated parameters and thus allow for estimation of the largest Lyapunov exponent, model error and limit value of the predictability curve. The correction is based on comparing the parameters estimated for the Lorenz's and ECMWF and on comparison with the largest Lyapunov exponent (λ=0,35 day-1 ) and limit value of the predictability curve (E∞=8,2) of the Lorenz's model. Parameters are calculated from approximations made by the Quadratic hypothesis with and without model error, as well as by Logarithmic and General hypotheses and by hyperbolic tangent employing corrections with and without model error. Average value of the largest Lyapunov exponent is estimated to be λ=0,37 day-1 for the ECMWF model, limit values of the predictability curves are estimated with lower theoretically derived values and new approach of calculation of model error based on comparison of models is presented.
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Analysis of Logistic Maps
Adeleke, Joshua Owolabi ; Šremr, Jiří (referee) ; Řehák, Pavel (advisor)
Logistická mapa souvisí s diskrétní logistickou rovnicí. Na rozdíl od svého kontinuálního protějšku vykazuje logistická diferenční rovnice velmi komplikovanou dynamiku včetně chaotiky chování. Tato práce tak zkoumala kvalitativní chování logistické mapy podle pomocí některých matematických nástrojů. Tato dynamika byla studována systematicky, a to tak, aby její povaha byla čistá forma až do bodu, kdy bylo komplikované se s ní vypořádat, byly pečlivě studovány. dále pojem konjugace byl zaměstnán v okamžiku, kdy jeho analytický výpočet představoval být komplikovaný, s čímž byly dále odhaleny jeho vlastnosti. Byly učiněny pozoruhodné závěry, mezi nimiž je popis chaotického chování logistická mapa, jak ji odhaluje její spojení se stanovou mapou. V průběhu této studie tedy existuje další nástroj pro vyšetřování chaotického chování byla poznamenána logistická mapa, která je symbolickou dynamikou, se kterou se bude v budoucnu studovat logistická mapa může zabrat.
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Order and chaos in a simple model of molecular vibrations
Novotný, Jakub ; Stránský, Pavel (advisor) ; Kloc, Michal (referee)
In this work we join the struggle to find a connection between classical and quantum chaos. We study the classical chaos in the classical limit of a simple algebraic model of molecular vibrations, based on the dynamical symmetry of u(3) algebra. We employ several methods for the classical chaos analysis, namely the Lyapunov exponents, the Poincaré sections, and the chaotic fraction of the classical phase space. It is shown that the chaoticity of the model depends nontrivially both on the strength of the external field and on the energy of the system. This work prepares the ground for a future comparison of classical and quantum chaos indicators. 1
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Methods for electroencephalogram records comparison
Kliment, Juraj ; Ronzhina, Marina (referee) ; Janoušek, Oto (advisor)
The bachelor thesis deals with the comparison of EEG signals from the human brain. The aim of this work is to find suitable nonlinear parameters, based on which it is possible to compare EEG records created in different conditions. The selected parameters are then tested on data from a publicly available database using Matlab software, the results are statistically processed and compared with the results of existing scientific studies. The comparison was based on the parameters Approximate entropy, Correlation dimension, Hurst exponent and Lyapunov exponent.
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