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Planar dynamics of the mathematical pendulum
Rauš, Michal ; Tomášek, Petr (referee) ; Čermák, Jan (advisor)
This bachelor's thesis is focused on the mathematical modeling of a motion of simple and double pendulum with the use of an ordinary differential equations. It's main objectives are a derivation of equations of motion, an assessment of stability as well as periodic behaviour of respective models and graphical interpretation of achieved results.
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Continuous and discrete models of population biology
Fedorková, Lucie ; Tomášek, Petr (referee) ; Čermák, Jan (advisor)
This thesis analyzes the continuous and discrete logistic model of a single-species population. For both of these models, there are discussed problems of equilibria, their stability and behaviour of the solutions for different initial conditions. In the case of the discrete model, the periodic behaviour of solutions is discussed in detail with respect to change of a parameter characterizing growth of the investigated population. The chaotic behaviour of solutions is mentioned as well. The graphic interpretations of each of the problems are performed using the software MATLAB. The calculations are checked via the software Maple.
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The Lotka-Volterra population model and its generalizations
Zubková, Kateřina ; Tomášek, Petr (referee) ; Čermák, Jan (advisor)
This bachelor's thesis is focused on several dynamical systems of nonlinear differential equations originating from the Lotka-Volterra predator-prey model. The aim of the thesis is to discuss stability and attractivity of the singular solutions of the classical model and its generalizations, investigate its periodicity and impact of the change of the initial data and entry parameters on the system's behaviour. The attention is also paid to involvement of time delay into the studied models, and its influence of stability on singular solutions. From the formal viewpoint, the thesis contains description and application of main stability technique applied to these nonlinear models and testing of results on some data.
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Continuous and discrete models of population biology
Fedorková, Lucie ; Tomášek, Petr (referee) ; Čermák, Jan (advisor)
This thesis analyzes the continuous and discrete logistic model of a single-species population. For both of these models, there are discussed problems of equilibria, their stability and behaviour of the solutions for different initial conditions. In the case of the discrete model, the periodic behaviour of solutions is discussed in detail with respect to change of a parameter characterizing growth of the investigated population. The chaotic behaviour of solutions is mentioned as well. The graphic interpretations of each of the problems are performed using the software MATLAB. The calculations are checked via the software Maple.
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|
|
The Lotka-Volterra population model and its generalizations
Zubková, Kateřina ; Tomášek, Petr (referee) ; Čermák, Jan (advisor)
This bachelor's thesis is focused on several dynamical systems of nonlinear differential equations originating from the Lotka-Volterra predator-prey model. The aim of the thesis is to discuss stability and attractivity of the singular solutions of the classical model and its generalizations, investigate its periodicity and impact of the change of the initial data and entry parameters on the system's behaviour. The attention is also paid to involvement of time delay into the studied models, and its influence of stability on singular solutions. From the formal viewpoint, the thesis contains description and application of main stability technique applied to these nonlinear models and testing of results on some data.
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|
|
Planar dynamics of the mathematical pendulum
Rauš, Michal ; Tomášek, Petr (referee) ; Čermák, Jan (advisor)
This bachelor's thesis is focused on the mathematical modeling of a motion of simple and double pendulum with the use of an ordinary differential equations. It's main objectives are a derivation of equations of motion, an assessment of stability as well as periodic behaviour of respective models and graphical interpretation of achieved results.
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