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Lorenzův systém: cesta od stability k chaosu

The Lorenz system: A route from stability to chaos

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Author
Arhinful, Daniel Andoh
Advisor
Řehák, Pavel
Referee
Šremr, Jiří
Grade
D
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Abstract
The theory of deterministic chaos has generated a lot of interest and continues to be one of the much-focused research areas in the field of dynamics today. This is due to its prevalence in essential parts of human lives such as electrical circuits, chemical reactions, the flow of blood through the human system, the weather, etc. This thesis presents a study of the Lorenz equations, a famous example of chaotic systems. In particular, it presents the analysis of the Lorenz equations from stability to chaos and various bifurcation scenarios with numerical and graphical interpretations. It studies concepts of non-linear dynamical systems such as equilibrium points, stability, linearization, bifurcation, Lyapunov function, etc. Finally, it discusses how the Lorenz equations serve as a model for the waterwheel (in detail), and the convection roll for fluid.
 
The theory of deterministic chaos has generated a lot of interest and continues to be one of the much-focused research areas in the field of dynamics today. This is due to its prevalence in essential parts of human lives such as electrical circuits, chemical reactions, the flow of blood through the human system, the weather, etc. This thesis presents a study of the Lorenz equations, a famous example of chaotic systems. In particular, it presents the analysis of the Lorenz equations from stability to chaos and various bifurcation scenarios with numerical and graphical interpretations. It studies concepts of non-linear dynamical systems such as equilibrium points, stability, linearization, bifurcation, Lyapunov function, etc. Finally, it discusses how the Lorenz equations serve as a model for the waterwheel (in detail), and the convection roll for fluid.
 
Keywords
Lorenz equations, Non-linear systems, Equilibrium points, Stability, Linearization, Bifurcation, Lyapunov function, Waterwheel and Convection roll., Lorenz equations, Non-linear systems, Equilibrium points, Stability, Linearization, Bifurcation, Lyapunov function, Waterwheel and Convection roll.
Language
angličtina (English)
Study brunch
Matematické inženýrství
Composition of Committee
prof. RNDr. Josef Šlapal, CSc. (předseda) prof. RNDr. Miloslav Druckmüller, CSc. (místopředseda) doc. Ing. Luděk Nechvátal, Ph.D. (člen) doc. RNDr. Jiří Tomáš, Dr. (člen) doc. Mgr. Pavel Řehák, Ph.D. (člen) Prof. Bruno Rubino (člen) Assoc. Prof. Matteo Colangeli (člen) Assoc. Prof. Massimiliano Giuli (člen)
Date of defence
2020-07-16
Process of defence
Student introduced his diploma thesis The Lorenz system: A route from stability to chaosto the committee members and explained the fundaments of his topic. He answered the oponent's questions satisfactorily. The next question was from doc. Řehák and the answer was satisfactory.
Result of the defence
práce byla úspěšně obhájena
Persistent identifier
http://hdl.handle.net/11012/192316
Source
ARHINFUL, D. Lorenzův systém: cesta od stability k chaosu [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2020.
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  • 2020 [577]
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