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Lotka-Volterra competition model on graphs
Skácelová, Radka ; Šremr, Jiří (referee) ; Čermák, Jan (advisor)
This bachelor thesis analyzes several mathematical models describing the co-existence of two species, especially the classic Lotka-Volterra model and its extensions. These models are described by a system of non-linear differential equations. The goal of this thesis is to develop an extended predator-prey model using the graph theory, to find stationary states of this model and to analyze their stability. The thesis is furthermore focused on a comparison between the obtained results for this model with the existing results for the competition model on graphs.
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Advanced epidemic models and their analysis
Skácelová, Radka ; Šremr, Jiří (referee) ; Čermák, Jan (advisor)
This diploma thesis analyzes several SIR epidemiological models which are described by a system of non-linear differental equations; it is mainly focused on SIR models with biths and deaths describing long-term epidemics. The goal of this thesis is to develop and analyze models with a time delay, and to extend some of the studied models using the graph theory, find their stationary states and analyze their stability. The thesis is particularly focused on spatially heterogenous stationary states for special types of graphs - complete graphs, stars and cycles.
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Advanced epidemic models and their analysis
Skácelová, Radka ; Šremr, Jiří (referee) ; Čermák, Jan (advisor)
This diploma thesis analyzes several SIR epidemiological models which are described by a system of non-linear differental equations; it is mainly focused on SIR models with biths and deaths describing long-term epidemics. The goal of this thesis is to develop and analyze models with a time delay, and to extend some of the studied models using the graph theory, find their stationary states and analyze their stability. The thesis is particularly focused on spatially heterogenous stationary states for special types of graphs - complete graphs, stars and cycles.
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Lotka-Volterra competition model on graphs
Skácelová, Radka ; Šremr, Jiří (referee) ; Čermák, Jan (advisor)
This bachelor thesis analyzes several mathematical models describing the co-existence of two species, especially the classic Lotka-Volterra model and its extensions. These models are described by a system of non-linear differential equations. The goal of this thesis is to develop an extended predator-prey model using the graph theory, to find stationary states of this model and to analyze their stability. The thesis is furthermore focused on a comparison between the obtained results for this model with the existing results for the competition model on graphs.
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