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Periodic boundary value problem in mathematical models of nonlinear oscillators
Kyjovský, Adam ; Nechvátal, Luděk (referee) ; Šremr, Jiří (advisor)
This master's thesis deals with qualitative analysis of nonlinear differential equations of second order. For autonomous equations some basic notions of Hamiltonian systems (mainly construction of phase portrait) are presented. For non-autonomous equations the method of lower and upper functions for periodic boundary value problem is used. These notions are then applied to a model of mechanical oscillator, a question of existence of solutions to autonomous and non-autonomous nonlinear differential equations is studied.
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Analysis and circuit realization of special chaotic systems
Rujzl, Miroslav ; Hruboš, Zdeněk (referee) ; Petržela, Jiří (advisor)
This master‘s thesis deals with analysis of electronic dynamical systems exhibiting chaotic solution. In introduction, some basic concepts for better understanding of dynamical systems are explained. After introduction, current knowledge from the world of circuits exhibiting chaotic solutions are discussed. The best-known chaotic systems are analyzed numerically in Matlab software. Numerical analysis and experimental verification were demonstrated at C class transistor amplifier, which confirmed the chaotic behavior and generation of a strange attractor.
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Chimney demolition modeling
Ficker, Tomáš ; Keršner, Zbyněk (referee) ; Frantík, Petr (advisor)
The thesis deals with solving of a discrete dynamic 2D model of a chimney during its demolition. Specific goal of the thesis is to clarify observed phenomenon that is a break of the chimney while falling. The model of the chimney is designed and solved using software FyDiK which is able to solve dynamic effects. For verification of results, two models of chimney have been designed.
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Autonomous systems of differential equations - classical vs fractional ones
Glozigová, Anna ; Zatočilová, Jitka (referee) ; Nechvátal, Luděk (advisor)
Hlavním zaměřením této práce je hlubší studium a porovnání dvou oblastí diferenciálních rovnic, kde důraz je kladen na neceločíselné řády, neboť během posledních desítek let se tato oblast nejenže stala populární, ale dokonce bylo zjištěno, že standardní přístupy řešení nenaplňují očekávání, tudíž jsou vyžadovány speciální postupy. Práce také obsahuje příklady, experimenty a simulaci pro ověření, případné vyvrácení teoretických výsledků.
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Nonlinear dynamical systems and chaos
Tesař, Lukáš ; Opluštil, Zdeněk (referee) ; Nechvátal, Luděk (advisor)
The diploma thesis deals with nonlinear dynamical systems with emphasis on typical phenomena like bifurcation or chaotic behavior. The basic theoretical knowledge is applied to analysis of selected (chaotic) models, namely, Lorenz, Rössler and Chen system. The practical part of the work is then focused on a numerical simulation to confirm the correctness of the theoretical results. In particular, an algorithm for calculating the largest Lyapunov exponent is created (under the MATLAB environment). It represents the main tool for indicating chaos in a system.
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Design and realization of a new laboratory exercise with PLC B&R Automation
Cejpek, Zdeněk ; Němec, Zdeněk (referee) ; Lang, Stanislav (advisor)
This bachelor thesis is concerned with designing of a laboratory task primary dedicated for the course „Advanced control methods“, which for the education uses the instruments of company B&R Automation. From possible aproaches chooses modeling of dynamic systems using analog electrical circuits. Those circuits are realized in modular manner, in order to allow building models of various systems. The thesis also includes a desing of proper casing, which simplifies the manipulation by building of the systems. Using designed prototype modules, a model of a separately excited DC motor was built. This model is used for realization of the laboratory task, for which is provided a short manual including some basic program for Automation Studio. The thesis also briefly introduces the company B&R, it´s products and a PLC configuration used in courses „Advanced control methods“.
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Dynamical Simulation of a System with Contact Problem
Raisinger, Jan ; Keršner, Zbyněk (referee) ; Frantík, Petr (advisor)
This work deals with the simulation of a dynamical system with a contact problem represented by the contact of a bicycle tube with a tire during inflation and loading of a bicycle wheel. In the first part the work defines the basics of dynamical systems a contact problems and introduces the methods used for following simulations. The practical part of the work desribes the process of converting a real system of rim-tube-tire objects to a computional model by determining its geometry and material characteristics as a continuous object and its subsequent discretization, introduces the program used for the subsequent simulations (FyDiK 2D) and shows the results of said simulations.
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Multirobot Path Planning in a Dynamic System
Dokoupil, Ladislav ; Veigend, Petr (referee) ; Zbořil, František (advisor)
This thesis deals with the problem of dynamic environment search using multi-agent systems. The primary result of this work is participation in the MAPC2022 contest, but the application can be found in the exploration of unknown space, assuming finite visibility and unlimited distance of communication of the agents. After describing the current methods for solving the given problem and their limitations, an algorithm based on ant colony optimization is proposed. Graphs were then created with data from running program with various parameters. The result of work is agents synchronization improvements and overall optimization of the platform involved in the mentioned contest from previous year. As a result half more of explored space was measured compared to previous solution.
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