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Methods for electroencephalogram records comparison
Kliment, Juraj ; Ronzhina, Marina (oponent) ; Janoušek, Oto (vedoucí práce)
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 (oponent) ; Řehák, Pavel (vedoucí práce)
A logistic map is related to a discrete logistic equation. Unlike its continuous counterpart, a logistic difference equation exhibits very complicated dynamics including chaotic behavior. This work thus investigated the qualitative behavior of the logistic map by employing some mathematical tools. This dynamics was studied systematically, in such a way that its nature from the pure form to the point when it got complicated to deal with were studied closely. Furthermore, the concept of conjugacy was employed at the point when its analytic computation posed to be complicated, with which its characteristics were further revealed. Notable inferences were made, among which is the description of the chaotic behavior of the logistic map as revealed by its conjugacy with the tent map. Thus, in course of this study, other tool for investigating the chaotic behavior of the logistic map was remarked, which is the symbolic dynamic, with which future study on the logistic map can take up on.
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Methods for electroencephalogram records comparison
Kliment, Juraj ; Ronzhina, Marina (oponent) ; Janoušek, Oto (vedoucí práce)
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 (oponent) ; Nechvátal, Luděk (vedoucí práce)
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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Analýza a predikce vývoje devizových trhů pomocí chaotických atraktorů a neuronových sítí
Pekárek, Jan ; Dostál, Petr (oponent) ; Budík, Jan (vedoucí práce)
Práce se zabývá komplexní analýzou a predikcí devizových trhů. Využívá při tom pokročilých metod umělé inteligence, zejména neuronových sítí a teorie chaosu. Představuje netradiční přístupy a metody z každé z těchto oblastí, srovnává je a aplikuje na reálný problém. Jádrem práce je návrh a srovnání několika predikčních modelů založených na zcela odlišných principech a teoriích. Výsledkem je výběr nejvhodnějšího predikčního modelu, jenž nese označení NAR + H. Model je hodnocen dle více kritérií, jsou diskutovány jeho klady a zápory, vyčíslena přibližná očekávaná ziskovost a riziko. Veškeré analytické, predikční a dílčí algoritmy jsou implementovány ve vývojovém prostředí Matlabu a tvoří jednotnou knihovnu všech použitých funkcí a skriptů. Ta je zároveň druhým hlavním výstupem práce.
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Automatic Analysis of Heart Rate Variability Signals
Kubičková, Alena ; Halámek, Josef (oponent) ; Lhotská, Lenka (oponent) ; Kozumplík, Jiří (vedoucí práce)
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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Podobnosti chaotického chování Lorenzova 05 modelu a modelů ECMWF
Bednář, Hynek ; Raidl, Aleš (vedoucí práce) ; Jaňour, Zbyněk (oponent) ; Pokorný, Pavel (oponent)
Tato práce zkoumá schopnost Lorenzova chaotického modelu z roku 2005 simulovat křivky prediktability vypočtené z ročních průměrů denních dat numerického předpovědního modelu ECMWF z období 1986-|2011 a ukazuje podobnost těchto křivek Lorenzova modelu s počtem proměnných N = 90. Dále tato práce zkoumá aproximace křivek a diferencí křivek obou modelů s cílem korigovat parametry určené z aproximací modelu ECMWF a tím odhadnout největší Ljapunovův exponent, modelovou chybu a limitní hodnotu křivky prediktability tohoto modelu. Korekce je provedena na základě porovnání parametrů obou modelů a na základě porovnání s největším Ljapunovovým exponentem (λ=0,35 den-1 ) a limitní hodnotou křivky prediktability (E∞=8,2) Lorenzova modelu. Parametry jsou určeny z aproximací kvadratickou hypotézou s a bez modelové chyby, logaritmickou a obecnou hypotézou a hyperbolickým tangensem v úpravě s a bez modelové chyby. Výsledný odhad průměrné hodnoty největšího Ljapunovova exponentu modelu ECMWF je λ=0,37 den -1 , limitní hodnoty křivky prediktability jsou odhadnuty jako nižší, než je teoreticky prezentováno a na základě porovnání modelů je představena nová metoda určení modelové chyby.
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Analysis of Logistic Maps
Adeleke, Joshua Owolabi ; Šremr, Jiří (oponent) ; Řehák, Pavel (vedoucí práce)
A logistic map is related to a discrete logistic equation. Unlike its continuous counterpart, a logistic difference equation exhibits very complicated dynamics including chaotic behavior. This work thus investigated the qualitative behavior of the logistic map by employing some mathematical tools. This dynamics was studied systematically, in such a way that its nature from the pure form to the point when it got complicated to deal with were studied closely. Furthermore, the concept of conjugacy was employed at the point when its analytic computation posed to be complicated, with which its characteristics were further revealed. Notable inferences were made, among which is the description of the chaotic behavior of the logistic map as revealed by its conjugacy with the tent map. Thus, in course of this study, other tool for investigating the chaotic behavior of the logistic map was remarked, which is the symbolic dynamic, with which future study on the logistic map can take up on.
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Řád a chaos v jednoduchém modelu molekulárních vibrací
Novotný, Jakub ; Stránský, Pavel (vedoucí práce) ; Kloc, Michal (oponent)
Tato práce se připojuje k usilovnému hledání propojení mezi klasickým a kvantovým chaosem. Zabývá se analýzou klasického chaosu v klasické limitě kvantového modelu jed- noduchých molekulových vibrací, sestaveného na základě dynamických symetrií algebry u(3). Pro tento model adaptuje metody pro studium projevů klasického chaosu (Lyapu- novův exponent, Poincarého řezy, podíl chaotického objemu ve fázovém prostoru). Práce ukazuje, že chaotičnost modelu netriviálně závisí na síle vnějšího pole i na energii systému, a připravuje půdu pro porovnání s kvantovými indikátory chaosu. 1
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Methods for electroencephalogram records comparison
Kliment, Juraj ; Ronzhina, Marina (oponent) ; Janoušek, Oto (vedoucí práce)
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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