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Artificial Life Models
Ďuričeková, Daniela ; Martinek, David (referee) ; Peringer, Petr (advisor)
This bachelor thesis describes design and implementation of an artificial life simulator. The work is divided into four parts. The aim of the first part is to provide a brief overview of artificial life and related terminology. The second part deals with selected design patterns and the process of designing a simulation system, whose purpose is to simulate an ecosystem of artificial life entities. The subsequent part focuses on implementation of individual system components. Finally, the system is tested and evaluated on two sample models.
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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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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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Artificial Life Models
Ďuričeková, Daniela ; Martinek, David (referee) ; Peringer, Petr (advisor)
This bachelor thesis describes design and implementation of an artificial life simulator. The work is divided into four parts. The aim of the first part is to provide a brief overview of artificial life and related terminology. The second part deals with selected design patterns and the process of designing a simulation system, whose purpose is to simulate an ecosystem of artificial life entities. The subsequent part focuses on implementation of individual system components. Finally, the system is tested and evaluated on two sample models.
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Optimalizace těžby přírodních zdrojů
Chrobok, Viktor ; Dlouhý, Martin (advisor) ; Kodera, Jan (referee) ; Vošvrda, Miroslav (referee)
The thesis describes various modifications of the predator-prey model. The modifications are considering several harvesting methods. At the beginning a solution and a sensitivity analysis of the basic model are provided. The first modification is the percentage harvesting model, which could be easily converted to the basic model. Secondly a constant harvesting including a linearization is derived. A significant part is devoted to regulation models with special a focus on environmental applications and the stability of the system. Optimization algorithms for one and both species harvesting are derived and back-tested. One species harvesting is based on econometrical tools; the core of two species harvesting is the modified Newton's method. The economic applications of the model in macroeconomics and oligopoly theory are expanded using the methods derived in the thesis.
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Mathematical modelling of the population dynamics of hemiparasitic plants
SVĚTLÍKOVÁ, Petra
The hemiparasite-host interaction is rather complex, acting as parasitism belowground and as competition for light aboveground. Studies modelling this interaction are rare. The most recent model of the hemiparasite-host interaction was developed from the well-known Rosenzweig-MacArthur predator-prey model by Fibich et al. (2010). Here, I modied the light availability function of the model into a more general form and examined the hemiparasite-host coexistence along a productivity gradient of the environment. The behaviour of presented and analyzed model was shown to depend particularly on parameter g scaling light availability for hemiparasites at high host biomasses. While it suggested the host-hemiparasite coexistence only at intermediate productivities under low g, species could coexist even at high productivities under higher g.
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Těžba v Predator-Prey modelu
Chrobok, Viktor ; Lagová, Milada (advisor) ; Kalčevová, Jana (referee)
The paper is focused on the Predator-Prey model modified in the case of harvesting one or both populations. Firstly there is given a short description of the basic model and the sensitivity analysis. The first essential modification is percentage harvesting. This model could be easily converted to the basic one using a substitution. The next modification is constant harvesting. Solving this system requires linearization, which was properly done and brought valuable results applicable even for the basic or the percentage harvesting model. The next chapter describes regulation models, which could be used especially in applying environmental policies. All reasonable regulation models are shown after distinguishing between discrete and continuous harvesting. The last chapter contains an algorithm for maximizing the profit of a harvester using econometrical modelling tools.
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