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Dynamical analysis of bistable mechanical oscillator
Byrtus, M. ; Půst, Ladislav
The contribution deals with analysis of dynamical properties of 1 DOF bistable mechanical oscillator. First the mathematical model is formulated. The original mathematical model is approximated by Duffing equation as it is commonly used. These two models are compared and it is shown how they differ in both static and dynamical response. The dynamical response is studied using bifurcation analysis performed by brute force numerical integration in time domain to detect area of interest from dynamical point of view. Such a bistable mechanical system can appear in many technical applications and therefore the proper modelling plays a significant role.
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Experimental measuring of Siemens mechatronic device.
Koláček, Martin ; Houfek, Lubomír (referee) ; Koláčný, Josef (advisor)
The aim of this work is experimental measurement followed by acquisition and reconstruction of data from the image format. Experimental work is focused on verifying properties of a real electric drive with synchronous motor and frequency converter. Special attention is paid to the influence of system parameters on the time flow of monitored values. There is also solved backward reconstruction of the data during exporting of outputs from the measured system.
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Periodic solutions of ordinary differential equations
Mitro, Erik ; Janovský, Vladimír (advisor) ; Felcman, Jiří (referee)
The thesis deals with periodic solutions of ordinary differential equations and examining of their stability. We are mainly limited to scalar differential equations. The first chapter is devoted to the stability of periodic solutions that is related to the Poincaré map. The aim is to decide on the asymptotic stability/instability of the fixed point of this map. To this end we need to compute derivatives of the Poincaré map of the first order or, possibly, of the higher orders. In the second chapter we introduce the concept of bifurcation and we examine the population model. In the third chapter we briefly mention the Van der Pol oscillator i.e the system of two equations. We illustrate the theory by examples.
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Bifurcation in mathematical models in biology
Kozák, Michal ; Stará, Jana (referee)
Stationary, spatially inhomogenous solutions of reaction-diffusion systems are studied in this thesis. These systems appears in biological models based on a Tu- ring's idea of a diffusion driven instability. In the connection, a global behaviour of bifurcation branches of these stationary solutions is analyzed. The thesis in- sists on theory of differential equations and on (particularly topological) methods of nonlinear analysis. The existence, as well as non-compatness in one-dimensional space, of a bifurcation branch of general reaction-diffusion system leading to Tu- ring's efekt is proved. Further, a priori estimates of Thomas model are derived. The results tend to theorem, that forall diffusion coefficient from the preestab- lished set there exists at least one stacionary, spacially nontrivial solution of Tho- mas model.
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Bifurcation in mathematical models in biology
Kozák, Michal ; Kučera, Milan (advisor) ; Stará, Jana (referee)
Stationary, spatially inhomogenous solutions of reaction-diffusion systems are studied in this thesis. These systems appears in biological models based on a Tu- ring's idea of a diffusion driven instability. In the connection, a global behaviour of bifurcation branches of these stationary solutions is analyzed. The thesis in- sists on theory of differential equations and on (particularly topological) methods of nonlinear analysis. The existence, as well as non-compatness in one-dimensional space, of a bifurcation branch of general reaction-diffusion system leading to Tu- ring's efekt is proved. Further, a priori estimates of Thomas model are derived. The results tend to theorem, that forall diffusion coefficient from the preestab- lished set there exists at least one stacionary, spacially nontrivial solution of Tho- mas model.
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Biometry based on retinal videosequences
Oweis, Kamil ; Odstrčilík, Jan (referee) ; Kolář, Radim (advisor)
The biometric methods are the most advanced methods for recognition and verification of person identity. These methods are quite fast, safe and applicable in different situations. In this thesis is used a set of retinal scans taken with a video-ophtalmoscope. These pictures are further modified for next processing, first of all by convertion into black-andwhite binary image, in some cases was after that used a binary matrix for description of image. Afterwards was suggested comparison method of images from the database with reference image of the retina: method of overlap and shift. It was tested a set of blackand-white and then also grey images. All method calculations was realized in program Matlab of which outcome was determination of the most congruent image with reference image and evaluation of overall program accuracy.
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Bifurcations in contact problems with Coulomb friction
Ligurský, Tomáš ; Renard, Y.
To explore the bifurcation in this contact problem, we have taken uniform meshes with 4096, 16384, 65536 and 262144 triangles. We shall show that the bifurcation behaviour is more complex here. Branches 1 and 4 approach one another for finer meshes, and they disappear both for the finest mesh. Nevertheless, regarding the branching of the corresponding contact problem with forces h = (h1,h2) over the plane h1-h2, one can find it stable and convergent, again. \n
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Bifurcation Localization in Retina Images
Kvapilová, Aneta ; Drahanský, Martin (referee) ; Semerád, Lukáš (advisor)
This thesis deals with processing images of human retina. Its main goal is to create a system which is able to localize places important in a process of creating biometrical template - bifurcations and crossing of blood vessels. The first part focuses on biometrics in detail and explains certain concepts of this area. It also mentions the anatomy of the human eye focusing on retina. The second part provides detailed description of all the stages and algorithms that were necessary in the process of creation of the application.
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Bifurcation Localization in Retina Images
Pres, Martin ; Drahanský, Martin (referee) ; Semerád, Lukáš (advisor)
From biometrical point of view, main features of retina are fovea, optic nerve and blood vessel tree. Blood vessel tree is unique for each person and this biological feature is used in biometric systems for person-recognition by retinal images. This document describes methods for optic disc and fovea localization, method for vessel tree segmentation, which is based on well-known \emph{Matched filters} method and also describes method for localization of blood vessel bifurcations. Main goal of this thesis is creation of program which can automatically preprocess input image, segment blood vessels and localize vessel bifircations. The program is implemented in Java with OpenCV library.
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