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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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Self-excited oscillators in electronics
Grill, Jiří ; Dobis, Pavel (referee) ; Štrunc, Marian (advisor)
The aim of my bachelor´s project is to enter into characteristics self-excited oscillators, specifically focused on the Van der Pol oscillator. The Van der Pol oscillators produce oscillations which may be generated in nonlinear dynamic systems (autonomous or not). I also deal with periodical stationary states in the binary system, the derivation of the Van der Pol equation and analysis of its possible solution. The course of oscillations is monitored depending on its non-linearity, using computer simulation in programmes MatLab and C++ Builder 6 both for the homogenous equation (with zero right hand side term) and inhomogenous equation (with non-zero right hand side term). The latter refer to excited Van der Pol oscillator which exhibits also a chaotic regime.
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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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The Indication of Earth Faults in Overhead Lines
Pospíšil, Zdeněk ; Topolánek, David (referee) ; Toman, Petr (advisor)
This master´s thesis deals with the indication and localization of earth faults in overhead lines. Earth fault is the most frequently occurring type of fault in medium voltage overhead lines – it covers approx. 95% of all faults and is very difficult to indicate and localize them correctly and in time with currently available methods on the market. Therefore is very important to study earth fault and its indication, localization. The thesis consists of a theoretical and a practical part. The theoretical part deals with faults in overhead networks with different type of neutral grounding, mainly with one phase to the ground fault in the compensated, ungrounded, solidly grounded and via resistance grounded networks. Most of the theoretical part is dedicated to one phase to the ground fault in the compensated and ungrounded networks, where this type fault is called the earth fault. In the compensated and ungrounded networks is described in details behavior – voltage and current relations during both steady state and transient state earth fault. The theoretical part is further dedicated to detection methods of earth faults and their preconditions for use. There is described also in details the complete procedure of earth fault detection, which includes indication, unhealthy feeder determination and exact position or line section localization. End of the theoretical part is then focused on determination of accuracy requirements for measurement of basic quantities and computation of other parameters. The practical part deals with a work at medium distribution network model, which includes familiarization with the model, detailed verification of its functionality and behavior during the earth fault, obtaining faults records and algorithmization of methods: method of qu – diagram and method of first half - period, which are able to detect unhealthy feeder. This part of the thesis was put together based on a demand of company Mega, corp., which wanted to verify function of both above mentioned and by them not yet tested methods.
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Self-excited oscillators in electronics
Grill, Jiří ; Dobis, Pavel (referee) ; Štrunc, Marian (advisor)
The aim of my bachelor´s project is to enter into characteristics self-excited oscillators, specifically focused on the Van der Pol oscillator. The Van der Pol oscillators produce oscillations which may be generated in nonlinear dynamic systems (autonomous or not). I also deal with periodical stationary states in the binary system, the derivation of the Van der Pol equation and analysis of its possible solution. The course of oscillations is monitored depending on its non-linearity, using computer simulation in programmes MatLab and C++ Builder 6 both for the homogenous equation (with zero right hand side term) and inhomogenous equation (with non-zero right hand side term). The latter refer to excited Van der Pol oscillator which exhibits also a chaotic regime.
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