This thesis focuses on deterministic chaos and selected methods of chaos control. It briefly describes the matter of deterministic chaos and presents commonly used tools of analysis of dynamical systems exhibiting chaotic behavior. A list of frequently studied chaotic systems is presented and followed by a description of methods of chaos control and the optimization of these methods. The practical part is dedicated to the stabilization of two model systems and one real system with described methods.

Diplomová práce pojednává o teorii chaotických dynamických systémů, speciálně se pak zabývá Rösslerovým systémem. Kromě standardních výpočtů spojených s bifurkační analýzou se práce zaměřuje na problém stabilizace, konkrétně na stabilizaci rovnovážných bodů. Ke stabilizaci je využita základní metoda zpětnovazebního řízení s časovým zpožděním. Významnou část práce tvoří zavedení a implementace obecné metody pro hledání vhodné volby parametrů vedoucí k úspěšné stabiliaci. Dalším diskutovaným tématem je možnost synchronizace dvou Rösslerových systémů pomocí různých synchronizačních schémat.

This master's thesis deals with solving fractional-order ordinary differential equations by the Adomian decomposition method. A part of the work is therefore devoted to the theory of equations containing differential operators of non-integer order, especially the Caputo operator. The next part is devoted to the Adomian decomposition method itself, its properties and implementation in the case of Chen system. The work also deals with bifurcation analysis of this system, both for integer and non-integer case. One of the objectives is to clarify the discrepancy in the literature concerning the fractional-order Chen system, where experiments based on the use of the Adomian decomposition method give different results for certain input parameters compared with numerical methods. The clarification of this discrepancy is based on recent theoretical knowledge in the field of fractional-order differential equations and their systems. The conclusions are supported by numerical experiments, own code implementing the Adomian decomposition method on the Chen system was used.

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

The diploma thesis deals with the loss of stability of thin-walled flue pipe at coal power plant. The problem of thin-walled structures is their propensity to the loss of stability due to abnormal conditions, for example a vacuum, effect of wind, snow and earthquake. The purpose is to find the optimal deployment of reinforcements so that the model meets the requirements of EN 1993-1-6. This required an evaluation of unreinforced version of the model to identify weaknesses and subsequently other configurations for the application of reinforcement. For determining the resistance the flue pipe to the loss of stability used primarily to access linear bifurcation analysis based on linear analysis, possibly materially nonlinear analysis. The result of work is a design of reinforcement of pipeline which under the requirements of the standard meets the latest model with a reserve of approximately 20 %.

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.

En difficulté dans un système économique et managérial qui ne leur convient plus, certains cadres choisissent de quitter leur organisation pour devenir coach. Par-delà la normativité des transitions de carrière en sciences de gestion, nous montrons qu’il s’agit d’une bifurcation. Au sein du courant des Critical Management Studies et à partir d’une perspective foucaldienne du pouvoir, nous interprétons la bifurcation comme un processus de saturation lié aux effets de subjectivation de la gouvernementalité managériale. La bifurcation constitue une distanciation critique, notamment chez les jeunes managers et les managers à mi-vie, et amorce une microémancipation vers et par le coaching, via une réappropriation subjective de techniques de souci de soi. Cette recherche est basée sur un protocole de Grounded Theory et sur la méthode des récits de vie. L’attitude analytique mobilise des énoncés phénoménologiques, une thématisation a posteriori et une analyse critique de discours. Notre modèle théorique repose sur une population de 25 cadres devenus coachs et met en évidence un processus générique qui s’exprime différemment selon l’âge lors de la transition, selon le vécu de l’expérience professionnelle, le sexe ou encore le poste avant la transition (manager, consultant). / Some executives, facing an economical and managerial system that doesn’t suit them anymore, chose to leave their position in a structure to become coaches. Beyond the managerial norms of career change, we explain that it is a turning point. This change of career, within the Critical Management Studies movement, and with a Foucauldian power perspective, is interpreted here as them reaching saturation point, due to the effects of subjectivation related to managerial governmentality. Those former executives, especially young and middle-aged managers, find themselves gaining a critical detachment. Furthermore, we notice a phenomenon of microemancipation through being coached … in the training of becoming a coach, by reappropriating the techniques of the care of the self. This research process involves Grounded Theory and life narratives. Firstly, we worked on phenomenological texts, then on an a posteriori coding by themes, and finally on a critical discourse analysis. Our resulting theoretical framework is anchored on a population of 25 former executives who have become coaches. It underlines a generic process with differences related to criteria such as gender, age when the career change happens, previous professional experience and position (manager or consultant).

In this article we investigate a pitchfork bifurcation of the local attractor of a simple capsizing model proposed by Thompson. Although this is a very simple system it has a very complicate dynamic. We try to reveal some properties of this dynamic with modern numerical methods. For this reason we approximate stable and unstable manifolds which connect the steady states to obtain a complete understanding of the topology in the phase space. We also consider approximations of the Lyapunov Exponents (resp. Floquet Exponents) which indicates the pitchfork bifurcation.

Das Phänomen der Rissmusterentstehung stellt ein anschauliches und numerisch nachvollziehbares Beispiel für Strukturbildung dar. Im Rahmen der vorliegenden Arbeit gelang es, einfache dreidimensionale Rissmuster zu berechnen, die durch Zugspannungen infolge inhomogener Schrumpfung durch Wärme- oder Stofftransport wachsen. Aufgrund wechselseitiger Entlastung bleiben Risse oder Teile einer Rissfront zurück. Für idealisierte periodische Rissanordnungen wurden durch bruchmechanische Verzweigungsanalyse kritische Last- und Geometrieparameter berechnet, für die sich neben der Grundlösung eine weitere Lösung finden lässt. Dadurch konnte die Frage beantwortet werden, warum verschiedene Typen von Rissmustern entstehen. Untersucht wurden Rissmuster in trocknender Stärke und Basalt sowie Tunnelrisse zwischen Glasplatten. Dafür war es nötig, die Risskontur numerisch zu bestimmen, wofür ein neues iteratives Verfahren entwickelt wurde. Für Säulen bildende Rissmuster in Basalt und trocknender Stärke mit konstanten Säulendurchmessern, welche stationär getrieben wachsen, wurde gezeigt, dass entgegen der Annahme in der Literatur eine Verzweigungslösung für zusammenhängende dreidimensionale Rissmuster existiert. Die berechneten kritischen Rissabstände unterscheiden sich nur unwesentlich von denjenigen zweidimensionaler Rissmodelle. Zum Verständnis der Herausbildung der Basaltsäulen wurde ein neuer Mechanismus gefunden, für den die Wechselwirkung zwischen Riss- und Erstarrungsfront der flüssigen Lava eine wesentliche Rolle spielt. Mittels eines iterativen Verfahrens wurde dafür die Erstarrungsfront berechnet. Die Ergebnisse zeigen gute Übereinstimmung mit den experimentellen Werten. Die Durchmesser von Stärkesäulen und Basaltsäulen nehmen nach dem gleichen Potenzgesetz mit zunehmender Wachstumsgeschwindigkeit ab. Für Tunnelrisse sind die Rissabstände nahezu konstant, obwohl entgegen ursprünglicher Annahmen gezeigt werden konnte, dass diese instationär getrieben wachsen. Als Ursache dafür wurde die durch die Rissgeometrie stark reduzierte Wechselwirkung zwischen den Tunnelrissen erkannt. Der Rissabstand nimmt potenzartig mit Dicke der trocknenden Schicht zu. Mittels einer Skalenanalyse konnte gute Übereinstimmung mit den Experimenten gefunden werden. / Crack patterns are a remarkable example of pattern formation. In this work simple three-dimensional crack patterns where analysed that are driven by inhomogeneous shrinkage caused from heat or mass transport. Caused by mutual unloading, parts of the crack front stop to grow. For idealised periodically repeatable crack configurations through fracture mechanics bifurcation analysis critical loading or geometry parameters where calculated for which beside the basic solution (growth of all cracks) another solution is possible. Analysed were crack patterns in drying starch and basalt and tunnelling cracks between glass plates. For this it was necessary to calculate the crack contour numerically, for this a new iteration method was developed. For the connected crack patterns in starch and basalt that form columns, driven stationary, it could be shown that there exists a bifurcation solution. Agreement with experimental data was found by including the solidification front ahead the crack tips. For the tunnelling cracks the crack spacing is nearly constant also they are unsteadily driven. The crack spacing scales with a power law of the thickness of the drying layer. With a scaling analysis good agreement with experimental data was found.

A power system will experience voltage collapse when the loads increase up to a certain critical limit, where the system physically cannot support the amount of connected load. This point identified as a Saddle- Node Bifurcation (SNB), corresponds to a generic instability of parameterized differential equation models and represents the intersection point where different branches of equilibria meet. At this point the jacobian matrix of the system is singular and the system loses stability bringing the typical scenario of voltage collapse. To prevent voltage instability and collapse, the computation of the closest distance from a present operating point to the saddle-node bifurcation set can be used as a loadability index useful in power system operation and planning. The power margin is determined by applying the iterative or direct method described in [16]. Numerical examples of both methods applied to IEEE 9-bus system and IEEE 39-bus system shows that the iterative method is more reliable although it requires a longer computation time. The stability of the system is negatively affected in two ways when generators reach their reactive power limits: the voltage stability margin is deteriorated, or immediate voltage instability and collapse is produced.