Lorenzův systém: cesta od stability k chaosu
Loading...
Date
Authors
Arhinful, Daniel Andoh
Advisor
Referee
Mark
D
Journal Title
Journal ISSN
Volume Title
Publisher
Vysoké učení technické v Brně. Fakulta strojního inženýrství
ORCID
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.
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.
Description
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.
Citation
ARHINFUL, D. Lorenzův systém: cesta od stability k chaosu [online]. Brno: Vysoké učení technické v Brně. Fakulta strojního inženýrství. 2020.
Document type
Document version
Date of access to the full text
Language of document
en
Study field
Matematické inženýrství
Comittee
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)
prof. Mgr. Pavel Řehák, Ph.D. (člen)
Prof. Bruno Rubino (člen)
Assoc. Prof. Matteo Colangeli (člen)
Assoc. Prof. Massimiliano Giuli (člen)
Date of acceptance
2020-07-16
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 defence
práce byla úspěšně obhájena