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Dynamics of Models of Infectious Diseases
Machovičová, Tatiana ; Štoudková Růžičková, Viera (oponent) ; Čermák, Jan (vedoucí práce)
The subject of this bachelor's thesis is mathematical modelling in the epidemiological study of infectious diseases. The primary goal was to construct, characterize and analyze of the Kermack-McKendrick epidemic model. Furthermore, the stability of venereal disease models is analyzed, with focus on Acquired Immunodeficiency Syndrome (AIDS) and its treatment.
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The Lorenz system: A route from stability to chaos
Arhinful, Daniel Andoh ; Šremr, Jiří (oponent) ; Řehák, Pavel (vedoucí práce)
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.
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The Lorenz system: A route from stability to chaos
Arhinful, Daniel Andoh ; Šremr, Jiří (oponent) ; Řehák, Pavel (vedoucí práce)
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.
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Dynamics of Models of Infectious Diseases
Machovičová, Tatiana ; Štoudková Růžičková, Viera (oponent) ; Čermák, Jan (vedoucí práce)
The subject of this bachelor's thesis is mathematical modelling in the epidemiological study of infectious diseases. The primary goal was to construct, characterize and analyze of the Kermack-McKendrick epidemic model. Furthermore, the stability of venereal disease models is analyzed, with focus on Acquired Immunodeficiency Syndrome (AIDS) and its treatment.
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