Les travaux de recherche de ce mémoire porte sur l'étude d'une classe particulière de systèmes dynamiques hybrides (s.d.h.) à commutations autonomes, ces dernières étant engendrées par un phénomène d'hystérésis. Plus particulièrement, après avoir introduit le système mathématique étudié, une analyse de cette classe de s.d.h. est réalisée avec notamment une étude des cycles limites (équations qui les déterminent, stabilité) et des phénomènes de bifurcations (noeud-selle, doublement de période). L'existence de propriétés caractéristiques des systèmes chaotiques comme la sensibilité aux conditions initiales est également mise en avant de façons graphique et calculatoire (exposant de Lyapunov). Enfin, une partie optimisation paramétrique a aussi été traitée dans le but d'améliorer certaines performances du système. Tous ces résultats théoriques sont appliqués à un système thermique (thermostat à résistance d'anticipation) et à un système électronique (convertisseur statique) à l'aide du calcul forme (Maple), de l'analyse par intervalles (Proj2D) et de simulations numériques (Matlab)

<p>Background: Due to constant changes and unpredictability in a turbulent environment, the traditional way of planning does not seem to work anymore. Therefore, new approaches to the external and internal conditions need to develop in order to cope with the environmental turbulence. </p><p>Purpose: The purpose of this thesis is to define a turbulent environment and identify how an organisation can cope with this environment. Procedure: We have developed a frame of reference mainly consisting of theories regarding a turbulent environment and change. In addition, we have selected eight guiding factors, which we have used when studying, systemising, and comparing how contemporary literature suggests that an organisation can cope with a turbulent environment. </p><p>Results: The conclusions we have come to are that with a definition of the environment as being fast-changing and of chaotic nature, where the changes are continuous, emergent, small, big or somewhere in between, and where paradoxes play an important role, it is necessary to develop an organisational structure, leadership, human resource, and corporate culture, in which the objective always is to create dynamics and to build in an acceptance of change.</p>

<p> I uppsatsen "Chaos Paintball, en investerings- och finansieringsbedömning" har en undersökning gällande en nyinvestering och finansieringen avseende nya aktiviteter och en byggnad genomförts. Undersökningen har utförts genom att tre olika byggnadsalternativ har tagits i beaktande och beräkningar på byggnadsalternativen har gjorts. Företagets planerade aktiviteter har undersökts genom att, med hjälp av kalkyler, genomföra beräkningar. Detta har lett fram till en rekommendation om vilka aktiviteter som företaget bör genomföra och satsa på. Undersökningarna har gjorts genom att intervjua företagets ägare, en byggfirma, en bank samt beräkningar av olika investeringskalkyler. </p><p>Syftet med uppsatsen är att undersöka om det är ekonomiskt lönsamt för företaget att starta upp nya aktiviteter och att investera i en byggnad.</p><p>Vi har dragit slutsatsen att företaget bör genomföra alternativet där en varmdel byggs till i en befintlig byggnad. Vi gör även bedömningen att företaget har goda förutsättningar att lyckas med de tidigare verksamheterna samt att starta upp de nya aktiviteterna Stuntman för en dag och Hyper Hockey.  </p>

Computation methods based on the Wiener chaos expansion have been developed to study the behaviors of the aeroelastic system with randomparameters. It is proven that the discrete wavelet transformation is one ofthe most accurate and efficient numerical schemes for this uncertainty quantizationproblem. In this thesis, we propose the stochastic collocation methods(SCM), whichis a type of sampling method combining the strength of the MonteCarlo simulation and the stochastic Galerkin method. The convergence with respect to the number of the nodal points is investigated, and simulation results to aeroelastic models in the presence of uncertainty in the system parameter and due to the initial condition are reported. It is demonstrated that the accuracy of the SCM is comparable to those achieved by using the wavelet chaos expansion. However, the SCM is more straightforward, efficient and easy to implement. / Applied Mathematics

We outline a multiprocessor architecture that uses modular arithmetic to implement numerical computation with 900 bits of intermediate precision. A proposed prototype, to be implemented with off-the-shelf parts, will perform high-precision arithmetic as fast as some workstations and mini- computers can perform IEEE double-precision arithmetic. We discuss how the structure of modular arithmetic conveniently maps into a simple, pipelined multiprocessor architecture. We present techniques we developed to overcome a few classical drawbacks of modular arithmetic. Our architecture is suitable to and essential for the study of chaotic dynamical systems.

Studying chaotic behavior in nonlinear systems requires numerous computations in order to simulate the behavior of such systems. The Standard Map Machine was designed and implemented as a special computer for performing these intensive computations with high-speed and high-precision. Its impressive performance is due to its simple architecture specialized to the numerical computations required of nonlinear systems. This report discusses the design and implementation of the Standard Map Machine and its use in the study of nonlinear mappings; in particular, the study of the standard map.

Gegenstand dieser Arbeit ist die Untersuchung universeller Skalengesetze, die in gekoppelten chaotischen Systemen beobachtet werden. Ergebnisse werden erzielt durch das Ersetzen der chaotischen Fluktuationen in der Störungsdynamik durch stochastische Prozesse. <br /> <br /> Zunächst wird ein zeitkontinuierliches stochastisches Modell fürschwach gekoppelte chaotische Systeme eingeführt, um die Skalierung der Lyapunov-Exponenten mit der Kopplungsstärke (coupling sensitivity of chaos) zu untersuchen. Mit Hilfe der Fokker-Planck-Gleichung werden Skalengesetze hergeleitet, die von Ergebnissen numerischer Simulationen bestätigt werden. <br /> <br /> Anschließend wird der neuartige Effekt der vermiedenen Kreuzung von Lyapunov-Exponenten schwach gekoppelter ungeordneter chaotischer Systeme beschrieben, der qualitativ der Abstoßung zwischen Energieniveaus in Quantensystemen ähnelt. Unter Benutzung der für die coupling sensitivity of chaos gewonnenen Skalengesetze wird ein asymptotischer Ausdruck für die Verteilungsfunktion kleiner Abstände zwischen Lyapunov-Exponenten hergeleitet und mit Ergebnissen numerischer Simulationen verglichen.<br /> <br /> Schließlich wird gezeigt, dass der Synchronisationsübergang in starkgekoppelten räumlich ausgedehnten chaotischen Systemen einem kontinuierlichen Phasenübergang entspricht, mit der Kopplungsstärke und dem Synchronisationsfehler als Kontroll- beziehungsweise Ordnungsparameter. Unter Benutzung von Ergebnissen numerischer Simulationen sowie theoretischen Überlegungen anhand einer partiellen Differentialgleichung mit multiplikativem Rauschen werden die Universalitätsklassen der zwei beobachteten Übergangsarten bestimmt (Kardar-Parisi-Zhang-Gleichung mit Sättigungsterm, gerichtete Perkolation). / Subject of this work is the investigation of universal scaling laws which are observed in coupled chaotic systems. Progress is made by replacing the chaotic fluctuations in the perturbation dynamics by stochastic processes. <br /> <br /> First, a continuous-time stochastic model for weakly coupled chaotic systems is introduced to study the scaling of the Lyapunov exponents with the coupling strength (coupling sensitivity of chaos). By means of the the Fokker-Planck equation scaling relations are derived, which are confirmed by results of numerical simulations. <br /> <br /> Next, the new effect of avoided crossing of Lyapunov exponents of weakly coupled disordered chaotic systems is described, which is qualitatively similar to the energy level repulsion in quantum systems. Using the scaling relations obtained for the coupling sensitivity of chaos, an asymptotic expression for the distribution function of small spacings between Lyapunov exponents is derived and compared with results of numerical simulations. <br /> <br /> Finally, the synchronization transition in strongly coupled spatially extended chaotic systems is shown to resemble a continuous phase transition, with the coupling strength and the synchronization error as control and order parameter, respectively. Using results of numerical simulations and theoretical considerations in terms of a multiplicative noise partial differential equation, the universality classes of the observed two types of transition are determined (Kardar-Parisi-Zhang equation with saturating term, directed percolation).

Background: Due to constant changes and unpredictability in a turbulent environment, the traditional way of planning does not seem to work anymore. Therefore, new approaches to the external and internal conditions need to develop in order to cope with the environmental turbulence. Purpose: The purpose of this thesis is to define a turbulent environment and identify how an organisation can cope with this environment. Procedure: We have developed a frame of reference mainly consisting of theories regarding a turbulent environment and change. In addition, we have selected eight guiding factors, which we have used when studying, systemising, and comparing how contemporary literature suggests that an organisation can cope with a turbulent environment. Results: The conclusions we have come to are that with a definition of the environment as being fast-changing and of chaotic nature, where the changes are continuous, emergent, small, big or somewhere in between, and where paradoxes play an important role, it is necessary to develop an organisational structure, leadership, human resource, and corporate culture, in which the objective always is to create dynamics and to build in an acceptance of change.

Since the late 1960’s, the hydromechanical term turbulence has been a part of the business administration vocabulary, but until the late 1980’s and early 1990’s, a relatively small amount of research was dedicated to this field. These studies and more contemporary ones conclude that where the business environment is paradoxical and of fast- changing and chaotic nature, successful corporate strategies are shaped by strategic flexibility founded in high innovation rates, networks and alliances, and organisational elasticity and adaptiveness. From this perspective, the purpose of this study was to track and examine the strategy formation processes of a company operating in a turbulent context, and to contribute to an understanding of how these turbulent conditions can be managed. The study was conducted with a hermeneutic, systems- oriented, longitudinal case-study method and with a contextcontent- process perspective in which the process was the key factor. To a large extent, our conclusions coincide with those of other researchers. Forming multidimensional networks and alliances coloured by voluntary initiatives and full attention seem to be an extremely important contribution to survival in turbulent contexts. Nevertheless, it is equally important to break up and build new alliances as the initial objectives of the arrangement have expired or been reached. Furthermore, in contrast to other researchers’ observations, we conclude that high innovation rates do not necessarily lead to a greater potential to be successful in a turbulent context. The issue is instead to present a product offering flexible in itself developed and marketed by a flexible organisation. Innovation rates are decided by self-initiated and unofficial activity on part of the r&amp;d teams and other coworkers, and management’s task is to facilitate for this corporate creativity to develop.

Today's product development process should be rapid andcost-efficient, and should result in innovative and reliableproducts. A crucial factor is the dynamic behaviour of theproduct. This thesis focuses on theoretical, numerical andexperimental approaches to achieve a comprehensiveunderstanding of dynamical phenomena occurring in nonlinearproducts, especially in products with parts that includeimpacts. The aim is to show the usefulness of nonlineartheories to better understand and optimise the dynamicbehaviour of products and thereby account for nonlinearphenomena already in the product development process. This is achieved through an investigation of researchefforts in the field of nonlinear dynamics; identification ofimportant research directions; a study on the effect ofcouplings between nonlinear parts; a detailed study on thedynamic behaviour of a product component; investigations oflow-cost strategies for controlling the dynamics of a nonlinearsystem; and the design and implementation of experimentalset-ups of two studied products. The investigation of research efforts shows that nonlinearparts are frequently included in products. Most common areparts that are nonlinear due to impacts and friction. Twoimportant areas are identified; to study coupling effectsbetween nonlinear subsystems and to study how nonlinearanalysis can be used to improve existing designs. Considering the studied products; a pantograph on a trainand a Braille printer, it can be concluded that thecharacteristics of a part can largely affect the dynamicbehaviour of the product. Typical nonlinear behaviour, such ascoexisting solutions and irregular motions, do occur. Theanalysis of the pan- tograph motion shows important aspects toconsider in the modelling process; coupling effects. In thecase of the Braille printer it is shown possible to create alow-cost control, by taking advantage of an existingdiscontinuity, to achieve a desired motion. Altogether, this work contributes to improved understandingof the be- haviour of nonlinear parts in products, especiallythose including impacts, pro- viding greater knowledge aboutaspects to consider in the design process. Keywords:Nonlinear Dynamics, Impacts, Discontinuities,Subsystems, Chaos, Irregular Behaviour, Printer Dynamics,Suspensions, Coupled Systems, Control. / QC 20100621