|
|
Difference calculus and difference equations
Bukotin, Denys ; Opluštil, Zdeněk (referee) ; Řehák, Pavel (advisor)
This thesis deals with application of difference equations for describing real processes. The aim of this work is to show the applicability of this kind of equations for solving some problems. We define some concepts of difference calculus, theory of difference equations and stability theory, also we show some similarities with theory of differential equations. Then we investigate a particular mathematical model and the behavior of its solutions. We examine Nicholson-Bailey model, as an example of population models and we show that difference equations are a useful tool for describing real processes.
|
|
|
Applications of ordinary differential equations with boundary conditions
Felixová, Lucie ; Opluštil, Zdeněk (referee) ; Čermák, Jan (advisor)
This bachelor's thesis is concerned with the applications of ordinary differential equations with boundary conditions. The aim of this thesis is to find the solution of straight bar stability under different boundary conditions (hinging, clamping and their combinations), of bended bars under horizontal loading and of straight bars on an elastic foundation (Winkler's foundation). Further, the thesis deals with the derivation of the equation for temperature field in a thin rod and for mathematical pendulum.
|
|
| |
|
|
Mathematical models in biology
Vidová, Katarína ; Šremr, Jiří (referee) ; Opluštil, Zdeněk (advisor)
The focus of this thesis is on a model construction from the field of mathematical biology describing interaction predator-prey. The most elementary Lotka–Volterra model is compared with more realistic models, i.e. intraspecific competition model and Gause model. Finally, the models are applied in specific situations and solution trajectories are drawn using Matlab.
|
|
|
Traffic flow modelling
Ježková, Jitka ; Opluštil, Zdeněk (referee) ; Kisela, Tomáš (advisor)
Tato diplomová práce prezentuje problematiku dopravního toku a jeho modelování. Zabývá se především několika LWR modely, které následně rozebírá a hledá řešení pro počáteční úlohy. Ukazuje se, že ne pro všechny počáteční úlohy lze řešení definovat na celém prostoru, ale jen v určitém okolí počáteční křivky. Proto je dále odvozena metoda výpočtu velikosti tohoto okolí a to nejen zcela obecně, ale i pro dané modely. Teoretický rozbor LWR modelů a řešení počátečních úloh jsou demonstrovány několika příklady, které zřetelně ukazují, jak se dopravní tok simulovaný danými modely chová.
|
|
|
Analysis of fractional-order two-dimensional models
Šustková, Apolena ; Opluštil, Zdeněk (referee) ; Nechvátal, Luděk (advisor)
This bachelor's thesis deals with the analysis of fractional-order two-dimensional models. The analysis itself is preceded by the introduction to the basic issues concerning the integer-order and fractional-order theory. Investigations are carried out for two specific models, Lotka-Volterra model and the Brusselator, the focus is put primarily on stability of the equilibrium points. The results are supported by appropriate phase portraits that were, for the non-integer case, created using the code for numerical solution of fractional differential equations.
|
|
|
Synchronization of chaotic dynamical systems
Borkovec, Ondřej ; Opluštil, Zdeněk (referee) ; Tomášek, Petr (advisor)
Diplomová práce pojednává o chaotických dynamických systémech se zvláštním zaměřením na jejich synchronizaci. Proces synchronizace je aplikován použitím dvou různých metod, a to - metodou úplné synchronizace na dva Lorenzovy systémy a metodou negativní zpětné vazby na dva Rösslerovy systémy. Dále je prozkoumána možná aplikace synchronizace chaotických systémů v oblasti soukromé komunikace, která je doplněná algoritmy v prostředí MATLAB.
|
|
|
Boundary problem for beam deflections
Machalová, Monika ; Šremr, Jiří (referee) ; Opluštil, Zdeněk (advisor)
This bachelor's thesis deals with the deflection of the beam. The second chapter is devoted to the linear differential equations and their solution, followed by a description of the different types of prescribed boundary conditions. In the third chapter the linear differential equation of second and fourth order for the deflection of the beam is derived. The last chapter is focused on comparing linear and nonlinear models. The theory is complemented by some solved examples, in which analytical solutions are plotted by using mathematical software Matlab.
|
|
|
Mathematical modelling of flight dynamics
Resl, Ondřej ; Tomášek, Petr (referee) ; Opluštil, Zdeněk (advisor)
This thesis deals with the mathematical models which describe flight dynamics of rocket. It mainly discusses the problem of smooth landing under different conditions, but it also deals with the range of a rocket. Certain models are provided with numerical solutions. The thesis also contains theoretical introduction to given issue.
|
|
|
System of autonomous differential equations
Benáčková, Jana ; Tomášek, Petr (referee) ; Opluštil, Zdeněk (advisor)
In his work dealing with applications, systems theory of autonomous differential equations in biology to the analysis model of coexistence of two populations. Mathematical models are described in general non-linear autonomous system of differential equations. I introduced the classification of types of singular points that are important for the following solutions to specific models. In the last part is an overview of the most famous models of the two populations (predator × prey) and specific models for the communities of invertebrate animals and mammals.
|
guest ::
