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Hyde, Griffin Nicholas. "Investigation into the Local and Global Bifurcations of the Whirling Planar Pendulum." Thesis, Virginia Tech, 2019. http://hdl.handle.net/10919/91395.
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This thesis details the investigation into the Whirling Planar Pendulum system. The WPP is a pendulum that is spun around a vertical spin axis at a controllable horizontal offset. This dynamical system exhibits both local and global bifurcations. The local pitchfork bifurcation leads to the splitting of a single stable equilibrium point into three (two stable and one unstable), as the spin rate is increased. The global bifurcations lead to two independent types of chaotic oscillations which are induced by sinusoidal excitations. The types of chaos are each associated with one of two homoclinic orbits in the system's phase portraits. The onset of each type of chaos is investigated through Melnikov's Method applied to the system's Hamiltonian, to find parameters at which the stable and unstable manifolds intersect transversely, indicating the onset of chaotic motion. These results are compared to simulation results, which suggest chaotic motion through the appearance of strange attractors in the Poincaré maps. Additionally, evidence of the WPP system experiencing both types of chaos simultaneously was found, resulting in a merger of two distinct types of strange attractor.Master of Science
This report details the investigation into the Whirling Planar Pendulum system. The WPP is a pendulum that is spun around a vertical spin axis at a controllable horizontal offset. This system can be used to investigate what are known as local and global bifurcations. A local bifurcation occurs when the single equilibrium state (corresponding to the pendulum hanging straight down) when spun at low speeds, bifurcates into three equilibria when the spin rate is increased beyond a certain value. The global bifurcations occur when the system experiences sinusoidal forcing near certain equilibrium conditions. The resulting chaotic oscillations are investigated using Melnikov’s method, which determines when the sinusoidal forcing results in chaotic motion. This chaotic motion comes in two types, which cause the system to behave in different ways. Melnikov’s method, and results from a simulation were used to determine the parameter values in which the pendulum experiences each type of chaos. It was seen that at certain parameter values, the WPP experiences both types of chaos, supporting the observation that these types of chaos are not necessarily independent of each other, but can merge and interact.
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Natsheh, Ammar Nimer. "Analysis, simulation and control of chaotic behaviour and power electronic converters." Thesis, Loughborough University, 2008. https://dspace.lboro.ac.uk/2134/5739.
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The thesis describes theoretical and experimental studies on the chaotic behaviour of a peak current-mode controlled boost converter, a parallel two-module peak current-mode controlled DC-DC boost converter, and a peak current-mode controlled power factor correction (PFC) boost converter. The research concentrates on converters which do not have voltage control loops, since the main interest is in the intrinsic mechanism of chaotic behaviour. These converters produce sub-harmonics of the clock frequency at certain values of the reference current I[ref] and input voltage V[in], and may behave in a chaotic manner, whereby the frequency spectrum of the inductor becomes continuous. Non-linear maps for each of the converters are derived using discrete time modelling and numerical iteration of the maps produce bifurcation diagrams which indicate the presence of subharmonics and chaotic operation. In order to check the validity of the analysis, MATLAB/SIMULINK models for the converters are developed. A comparison is made between waveforms obtained from experimental converters, with those produced by the MATLAB/SIMULINK models of the converters. The experimental and theoretical results are also compared with the bifurcation points predicted by the bifurcation diagrams. The simulated waveforms show excellent agreement, with both the experimental waveforms and the transitions predicted by the bifurcation diagrams. The thesis presents the first application of a delayed feedback control scheme for eliminating chaotic behaviour in both the DC-DC boost converter and the PFC boost converter. Experimental results and FORTRAN simulations show the effectiveness and robustness of the scheme. FORTRAN simulations are found to be in close agreement with experimental results and the bifurcation diagrams. A theoretical comparison is made between the above converters controlled using delayed feedback control and the popular slope compensation method. It is shown that delayed feedback control is a simpler scheme and has a better performance than that for slope compensation.
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Guo, Yu. "BIFURCATION AND CHAOS OF NONLINEAR VIBRO-IMPACT SYSTEMS." OpenSIUC, 2013. https://opensiuc.lib.siu.edu/dissertations/725.
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Vibro-impact systems are extensively used in engineering and physics field, such as impact damper, particle accelerator, etc. These systems are most basic elements of many real world applications such as cars and aircrafts. Such vibro-impact systems possess both the continuous characteristics as continuous dynamical systems and discrete characteristics introduced by impacts at the same time. Thus, an appropriately developed discrete mapping system is required for such vibro-impact systems in order to simplify investigation on the complexity of motions. In this dissertation, a few vibro-impact oscillators will be investigated using discrete maps in order to understand the dynamics of vibro-impact systems. Before discussing the nonlinear dynamical phenomena and behaviors of these vibro-impact oscillators, the theory for nonlinear discrete systems will be applied to investigate a two-dimensional discrete system (Henon Map). And the complete dynamics of such a nonlinear discrete dynamical system will be presented using the inversed mapping method. Neimark bifurcations in such a discrete system have also drawn a lot of interest to the author. The Neimark bifurcations in such a system have actually formed a boundary dividing the stable solution of positive and negative maps (inversed mapping). For the first time, one is able to obtain a complete prediction of both stable and unstable solutions in such a discrete dynamical system. And a detailed parameter map will be presented to illustrate how changes of parameters could affect the different solutions in such a system. Then, the theory of discontinuous dynamical systems will be adopted to investigate the vibro-impact dynamics in several vibro-impact systems. First, the bouncing ball dynamics will be analytically discussed using a single discrete map. Different types of motions (periodic and chaotic) will be presented to understand the complex behavior of this simple model. Analytical condition will be expressed using switching phase of the system in order to easily predict stick and grazing motion. After that, a horizontal impact damper model will be studied to show how complex periodic motions could be developed analytically. Complete set of symmetric and asymmetric periodic motions can also be easily predicted using the analytical method. Finally, a Fermi-Accelerator being excited at both ends will be discussed in detail for application. Different types of motions will be thoroughly studied for such a vibro-impact system under both same and different excitations.
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Kumeno, Hironori. "Bifurcation and Synchronization in Parametrically Forced Systems." Thesis, Toulouse, INSA, 2012. http://www.theses.fr/2012ISAT0024/document.
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Dans cette thèse, nous étudions un système à temps discret de dimension N, dont les paramètres varient périodiquement. Le système de dimension N est construit à partir de n sous-systèmes de dimension un couplés symétriquement. Dans un premier temps, nous donnons les propriétés générales du système de dimension N. Dans un second temps, nous étudions le cas particulier où le sous-système de dimension un est défini à l’aide d’une transformation logistique. Nous nous intéressons plus particulièrement à la structure des bifurcations lorsque N=1 ou 2. Des zones échangeurs centrées sur des points cuspidaux sont obtenues dans le cas de courbes de bifurcation de type fold (noeud-col).Ensuite, nous nous intéressons au comportement de circuits de type Chua couplés lorsqu’un paramètre varie lui aussi périodiquement, la période étant celle d’une des variables d’état interne au système. A partir de l’étude des bifurcations du système, la non existence de cycles d’ordre impair et la coexistence de plusieurs attracteurs est mise en évidence. D’autre part, on peut mettre en évidence la coexistence de différents attracteurs pour lesquels les états de synchronisation sont distincts. Le cas continu est comparé avec le cas discret. Des phénomènes tout à fait similaires sont obtenus. Il est important de noter que l’étude d’un système à temps discret est plus facile et plus rapide que celle d’un système à temps continu. L’étude du premier système permet donc d’avoir des informations sur ce qui peut se produire dans le cas continu. Pour terminer, nous analysons le comportement d’un autre système couplé à temps continu, basé lui aussi sur le circuit de Chua, mais pour lequel la commutation qui contrôle la variation du paramètre s’effectue différemment du premier système. Ce type de commutation génère une augmentation du nombre d’attracteursIn this thesis, we propose a N-dimensional coupled discrete-time system whose parameters are forced into periodic varying, the N-dimensional system being constructed of n same one-dimensional subsystems with mutually influencing coupling and also coupled continuous-time system including periodically parameter varying which correspond to the periodic varying in the discrete-time system.Firstly, we introduce the N-dimensional coupled parametrically forced discrete-time system and its general properties. Then, when logistic maps is used as the one-dimensional subsystem constructing the system, bifurcations in the one or two-dimensional parametrically forced logistic map are investigated. Crossroad area centered at fold cusp points regarding several order cycles are confirmed.Next, we investigated behaviors of the coupled Chua's circuit whose parameter is forced into periodic varying associated with the period of an internal state value. From the investigation of bifurcations in the system, non-existence of odd order cycles and coexistence of different attractors are observed. From the investigation of synchronizations coexisting of many attractors whose synchronizations states are different are observed. Observed phenomena in the system is compared with the parametrically forced discrete-time system. Similar phenomena are confirmed between the parametrically forced discrete-time system and the parametrically forced Chua's circuit. It is worth noting that this facilitates to analyze parametrically forced continuous-time systems, because to analyze discrete-time systems is easier than continuous-time systems. Finally, we investigated behaviors of another coupled continuous-time system in which Chua's circuit is used, while, the motion of the switch controlling the parametric varying is different from the above system. Coexisting of many attractors whose synchronizations states are different are observed. Comparing with theabove system, the number of coexisting stable state is increased by the effect of the different switching motion
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Abashar, Mohd Elbashir E. "Bifurcation, instability and chaos in fluidized bed catalytic reactors." Thesis, University of Salford, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.386532.
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Salih, Rizgar Haji. "Hopf bifurcation and centre bifurcation in three dimensional Lotka-Volterra systems." Thesis, University of Plymouth, 2015. http://hdl.handle.net/10026.1/3504.
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This thesis presents a study of the centre bifurcation and chaotic behaviour of three dimensional Lotka-Volterra systems. In two dimensional systems, Christopher (2005) considered a simple computational approach to estimate the cyclicity bifurcating from the centre. We generalized the technique to estimate the cyclicity of the centre in three dimensional systems. A lower bounds is given for the cyclicity of a hopf point in the three dimensional Lotka-Volterra systems via centre bifurcations. Sufficient conditions for the existence of a centre are obtained via the Darboux method using inverse Jacobi multiplier functions. For a given centre, the cyclicity is bounded from below by considering the linear parts of the corresponding Liapunov quantities of the perturbed system. Although the number obtained is not new, the technique is fast and can easily be adapted to other systems. The same technique is applied to estimate the cyclicity of a three dimensional system with a plane of singularities. As a result, eight limit cycles are shown to bifurcate from the centre by considering the quadratic parts of the corresponding Liapunov quantities of the perturbed system. This thesis also examines the chaotic behaviour of three dimensional Lotka-Volterra systems. For studying the chaotic behaviour, a geometric method is used. We construct an example of a three dimensional Lotka-Volterra system with a saddle-focus critical point of Shilnikov type as well as a loop. A construction of the heteroclinic cycle that joins the critical point with two other critical points of type planar saddle and axial saddle is undertaken. Furthermore, the local behaviour of trajectories in a small neighbourhood of the critical points is investigated. The dynamics of the Poincare map around the heteroclinic cycle can exhibit chaos by demonstrating the existence of a horseshoe map. The proof uses a Shilnikov-type structure adapted to the geometry of these systems. For a good understanding of the global dynamics of the system, the behaviour at infinity is also examined. This helps us to draw the global phase portrait of the system. The last part of this thesis is devoted to a study of the zero-Hopf bifurcation of the three dimensional Lotka-Volterra systems. Explicit conditions for the existence of two first integrals for the system and a line of singularity with zero eigenvalue are given. We characteristic the parameters for which a zero-Hopf equilibrium point takes place at any points on the line. We prove that there are three 3-parameter families exhibiting such equilibria. First order of averaging theory is also applied but we show that it gives no information about the possible periodic orbits bifurcating from the zero-Hopf equilibria.
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Hughes, Ryan Patrick. "Nonsmooth Bifurcations and the Role of Density Dependence in a Chaotic Infectious Disease Model." Thesis, Virginia Tech, 2020. http://hdl.handle.net/10919/96567.
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Discrete dynamical systems can exhibit rich and interesting dynamics at lower dimensions (and co-dimensions) than that of ODE models. Classically, the minimal dimension to observe chaotic behavior in an ODE model is three; whereas it can be achieved in a one-dimensional discrete map. It is often the choice of mathematical biologists to use discrete systems as it fills many roles such as sparse data, incorporation of life cycle stages and noisy measurements. This work is analyzes a discrete time model of an infected salmon population. It provides an in-depth analysis of non-smooth bifurcations for alternate functional forms for density dependence in the growth function of a given model. These demonstrate interesting structures and chaotic behaviors with biologically feasible interpretations such as intrinsic growth rate and probability of death. The choice of density dependence function, as well as parameterization, leads to whether chaos occurs or not.Master of Science
Often times biological processes do not happen in a continuous streamlined chain of events. We observe discrete life stages, ages, and morphological differences. Similarly, data is generally collected in discrete (and often fixed) time intervals. This work focuses on the role that population density has on the behavior of these systems. We dive into a case study for a viral infection in a salmon population. We show chaotic behavior can be observed as low as a single dimension model and discuss the biological implications. Additionally, we show that the choice of density dependence in a given infectious disease model directly impacts disease dynamics and can allow or prohibit chaotic behavior.
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Gaunersdorfer, Andrea, Cars H. Hommes, and Florian O. O. Wagener. "Bifurcation routes to volatility clustering." SFB Adaptive Information Systems and Modelling in Economics and Management Science, WU Vienna University of Economics and Business, 2000. http://epub.wu.ac.at/522/1/document.pdf.
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A simple asset pricing model with two types of adaptively learning traders, fundamentalists and technical analysts, is studied. Fractions of these trader types, which are both boundedly rational, change over time according to evolutionary learning, with technical analysts conditioning their forecasting rule upon deviations from a benchmark fundamental. Volatility clustering arises endogenously in this model. Two mechanisms are proposed as an explanation. The first is coexistence of a stable steady state and a stable limit cycle, which arise as a consequence of a so-called Chenciner bifurcation of the system. The second is intermittency and associated bifurcation routes to strange attractors. Both phenomena are persistent and occur generically in nonlinear multi-agent evolutionary systems. (author's abstract)Series: Working Papers SFB "Adaptive Information Systems and Modelling in Economics and Management Science"
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Welsh, S. C. "Generalised topological degree and bifurcation theory." Thesis, University of Glasgow, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.372419.
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何振林 and Albert Ho. "Chaos theory and security analysis." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1991. http://hub.hku.hk/bib/B31264931.
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Ho, Albert. "Chaos theory and security analysis /." [Hong Kong] : University of Hong Kong, 1991. http://sunzi.lib.hku.hk/hkuto/record.jsp?B13055227.
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Melbourne, I. "Bifurcation problems with octahedral symmetry." Thesis, University of Warwick, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.383295.
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Tesař, Lukáš. "Nelineární dynamické systémy a chaos." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2018. http://www.nusl.cz/ntk/nusl-392844.
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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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McGarry, John Kevin. "Application of bifurcation theory to physical problems." Thesis, University of Leeds, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.252925.
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Gomez, Maria Gabriela Miranda. "Symmetries in bifurcation theory : the appropriate context." Thesis, University of Warwick, 1992. http://wrap.warwick.ac.uk/110618/.
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Many phenomena in nature can be modeled by differential equations depending on parameters that are being varied continuously. We say that a given solution undergoes a bifurcation with respect to a given parameter if the qualitative behaviour of the system changes arbitrarily close to this solution when the parameter is varied across a critical value. Bifurcation problems can achieve a very high level of complexity because nature is complex. Several assumptions can be made in order to introduce considerable simplifications without going too far from reality. In this thesis we are mainly concerned in setting the problem in a symmetric context and showing that this is a realistic assumption that makes analysis much simpler. We want to emphasize that a lot of behaviour can be much easier to understand and predict when the appropriate symmetry context has been set. The message in part I of this thesis is that the full set of symmetries is not always obvious. We give examples of phenomena that are modeled by partial differential equations on rectangular domains and show that these problems have more than rectangular symmetry. Such hidden symmetries are found by embedding our problem into a larger one satisfying periodic boundary conditions and then consider all the symmetries that satisfy the original boundary conditions. In part II we study the behaviour of an electric circuit which can be modeled by a 3-dimensional system of ordinary differential equations. We begin by analysing this system under a symmetry assumption. Then in order to be more realistic we break the symmetry with a small perturbation. Most of the results for the asymmetric system are obtained by numerical and experimental search since a rigorous analysis became much harder. We observe a smooth change in qualitative behaviour by increasing the symmetry breaking perturbation. There is no dramatic change and we conclude that the original symmetry assumption was convenient and not misleading.
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Lari-Lavassani, Ali. "Multiparameter bifurcation with symmetry via singularity theory /." The Ohio State University, 1990. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487683049377079.
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Avrutin, Viktor [Verfasser]. "Bifurcation structures within robust chaos: computational aspects, numerical investigation and analytical explanation / Viktor Avrutin." Aachen : Shaker, 2011. http://d-nb.info/1075437423/34.
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Kennedy, R. Scott. "Synthesis of chaos theory & design." Thesis, Virginia Tech, 1994. http://hdl.handle.net/10919/42000.
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The design implications of chaos theory are explored. What does this theory mean, if anything, to landscape architecture or architecture?
In order to investigate these questions, the research was divided into four components relevant to design. First, philosophical- chaos offers a nonlinear understanding about place and nature. Second, aesthetical- fractals describe a deep beauty and order in nature. Thirdly, modeling-it is a qualitative method of modeling natural processes. Lastly, managing- concepts of chaos theory can be exploited to mimic processes found in nature. These components draw from applications and selected literature of chaos theory.
From these research components, design implications were organized and concluded. Philosophical implications, offer a different, nonlinear realization about nature for designers. Aesthetic conclusions, argue that fractal geometry can articulate an innate beauty (a scaling phenomenon) in nature. Modeling, discusses ways of using chaos theory to visualize the design process, a process which may be most resilient when it is nonlinear. The last research chapter, managing, applications of chaos theory are used to illustrate how complex form, like that in nature, can be created by designers.
Master of Landscape Architecture
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Kumeno, Hironori. "Bifurcation et synchronisation dans un système à paramétrisation forcée." Phd thesis, INSA de Toulouse, 2012. http://tel.archives-ouvertes.fr/tel-00749690.
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Dans cette thèse, nous étudions un système à temps discret de dimension N, dont les paramètres varient périodiquement. Le système de dimension N est construit à partir de n sous-systèmes de dimension un couplés symétriquement. Dans un premier temps, nous donnons les propriétés générales du système de dimension N. Dans un second temps, nous étudions le cas particulier où le sous-système de dimension un est défini à l'aide d'une transformation logistique. Nous nous intéressons plus particulièrement à la structure des bifurcations lorsque N=1 ou 2. Des zones échangeurs centrées sur des points cuspidaux sont obtenues dans le cas de courbes de bifurcation de type fold (nœud-col). Ensuite, nous nous intéressons au comportement de circuits de type Chua couplés lorsqu'un paramètre varie lui aussi périodiquement, la période étant celle d'une des variables d'état interne au système. A partir de l'étude des bifurcations du système, la non existence de cycles d'ordre impair et la coexistence de plusieurs attracteurs est mise en évidence. D'autre part, on peut mettre en évidence la coexistence de différents attracteurs pour lesquels les états de synchronisation sont distincts. Le cas continu est comparé avec le cas discret. Des phénomènes tout à fait similaires sont obtenus. Il est important de noter que l'étude d'un système à temps discret est plus facile et plus rapide que celle d'un système à temps continu. L'étude du premier système permet donc d'avoir des informations sur ce qui peut se produire dans le cas continu. Pour terminer, nous analysons le comportement d'un autre système couplé à temps continu, basé lui aussi sur le circuit de Chua, mais pour lequel la commutation qui contrôle la variation du paramètre s'effectue différemment du premier système. Ce type de commutation génère une augmentation du nombre d'attracteurs.
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Manoel, Miriam Garcia. "Hidden symmetries in bifurcation problems : the singularity theory." Thesis, University of Warwick, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.327556.
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Koperski, Jeffrey David. "Defending chaos: An examination and defense of the models used in chaos theory /." The Ohio State University, 1997. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487945015616055.
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Thweatt-Bates, Jennifer Jeanine. "Chaos theory and the problem of evil." Online full text .pdf document, available to Fuller patrons only, 2002. http://www.tren.com.
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Kateregga, George William. "Bifurcations in a chaotic dynamical system." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2019. http://www.nusl.cz/ntk/nusl-401527.
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Dynamical systems possess an interesting and complex behaviour that have attracted a number of researchers across different fields, such as Biology, Economics and most importantly in Engineering. The complex and unpredictability of nonlinear customary behaviour or the chaotic behaviour, makes it strange to analyse them. This thesis presents the analysis of the system of nonlinear differential equations of the so--called Lu--Chen--Cheng system. The system has similar dynamical behaviour with the famous Lorenz system. The nature of equilibrium points and stability of the system is presented in the thesis. Examples of chaotic dynamical systems are presented in the theory. The thesis shows the dynamical structure of the Lu--Chen--Cheng system depending on the particular values of the system parameters and routes to chaos. This is done by both the qualitative and numerical techniques. The bifurcation diagrams of the Lu--Chen--Cheng system that indicate limit cycles and chaos as one parameter is varied are shown with the help of the largest Lyapunov exponent, which also confirms chaos in the system. It is found out that most of the system's equilibria are unstable especially for positive values of the parameters $a, b$. It is observed that the system is highly sensitive to initial conditions. This study is very important because, it supports the previous findings on chaotic behaviours of different dynamical systems.
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Abdelmoula, Mohamed. "Phénomènes non linéaires et chaos dans les systèmes d’énergie renouvelable – Application à une installation photovoltaïque." Thesis, Reims, 2017. http://www.theses.fr/2017REIMS001/document.
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Afin de satisfaire les besoins futurs en énergie et de réduire l’impact environnemental, l’application de l’énergie renouvelable propre a été récemment reconsidérée. Dans ce contexte, un intérêt croissant pour le système d’alimentation isolé a été mesuré.Le besoin de topologies de faible puissance alimentées par un générateur photovoltaïque, évitant l’utilisation de transformateur, accentue l’étude de systèmes d’alimentation autonomes de basse tension. D’où la nécessité d’étudier les stratégiesde contrôle associées garantissant la stabilité, la fiabilité et l’efficacité.À mesure que les systèmes d’alimentation autonome deviennent plus complexes, les non-linéarités jouent un rôle de plus en plus important dans le comportement du système. La modélisation doit refléter avec précision la dynamique des composants et du système. En outre, les outils d’analyse des systèmes dynamiques devraient être fiable, même dans différents régimes de fonctionnement, fournissant des prédictions précises du comportement de ces derniers. Ce travail est consacré à l’étude d’un système photovoltaïque autonome. La structure proposée se compose d’un panneau photovoltaïque, d’un hacheur et d’une charge connectée en cascade via un bus continu. Les efforts de recherche se concentrent sur le processus de modélisation et l’analyse de stabilité du système. Une implémentation avec une description complète du modèle est ainsi détaillée est validé epar des résultats de simulation. Après avoir donné l’état de l’art, le manuscrit est divisé en quatre parties. Ces parties sont dédiées à la modélisation d’une installation photovoltaïque, à l’amélioration de la simulation numérique, et à l’étude de dynamique de ce système sous contrôles numériques.La thèse présente un aperçu des modèles de générateurs photovoltaïques. Ensuite,un modèle électrique modifié du panneau photovoltaïque est proposé. Nous avons également détaillé le processus de modélisation de l’installation photovoltaïque.Un solveur amélioré de modèle Differential-Algebraic Equations (DAEs) est ensuite développé. Une dixième approche de modélisation est aussi présentée. Nous avons également décrit le système photovoltaïque par un modèle discret simplifié. Ensuite, l’analyse de stabilité du système étudié est détaillée. En outre, nous avons étudié le comportement chaotique qui apparaît dans l’installation photovoltaïque basée sur le hacheur à deux cellules. Le but de la dernière partie est de montrer comment stabiliser l’orbite chaotique du système. Enfin, pour atteindre cet objectif, la commande par retour d’état retardé Time-Delayed Feedback Control (TDFC) est appliquéeIn order to satisfy future energy requirement and reduce environmental impact, application of clean renewable energy, have been reconsidered recently. In this context, a growing interest in isolated power system has been observed. The need of low power topologies fed by photovoltaic array avoiding the use oftransformer open the study of small-scale stand-alone power system. Hence, theneed to study the associated control design strategies ensuring stability, reliability and high efficiency.As systems become more complex, nonlinearities play an increasingly importantrole in stand-alone power system behaviour. Modeling must accurately reflect component and system dynamics. In addition, analysis tools should continue to workreliably, even under various system conditions, providing accurate predictions of systems behaviour.This work is devoted to the study of a stand-alone photovoltaic power system.The proposed structure consists on photovoltaic array, a dc-dc buck converter, anda load connected in cascade through a dc bus. The research efforts focus on themodeling process and stability analysis, which leads to an implementation with acomprehensive description validated through simulation results.After giving the state-of-the-art in second chapter, the manuscript is divided into four chapters. These parts are dedicated to photovoltaic plant modeling, the numeric simulation improvements and dynamic investigation of the photovoltaic system under digital controls.The thesis presents an overview of the photovoltaic generator models. Then, amodified photovoltaic array model is proposed. We also detailed the photovoltaic plant modeling process. An improved Differential-Algebraic Equations (DAEs)solver is then investigated. We also described the photovoltaic system by a simplified discrete model. Then, the dynamic stability analysis is detailled. In addition,we have studied the chaotic behaviour that appears in the photovoltaic plant basedon the two-cell dc-dc buck converter.The aim of the last part is to show, using control theory and numerical simulation,how to apply a method to stabilize the chaotic orbit. Finally, to accomplish this aim, a time-delayed feedback controller is used
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Kwok, Loong-Piu. "Viscous cross-waves: Stability and bifurcation." Diss., The University of Arizona, 1988. http://hdl.handle.net/10150/184441.
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In the first part of this thesis, the nonlinear Schrodinger equation for inviscid cross-waves near onset is found to be modified by viscous linear damping and detuning. The accompanying boundary condition at the wavemaker is also modified by damping from the wavemaker meniscus. The relative contributions of the free-surface, sidewalls, bottom, and wavemaker viscous boundary layers are computed. It is shown that viscous dissipation due to the wavemaker meniscus breaks the symmetry of the neutral curve. In the second part, existence and stability of steady solutions to the nonlinear Schrodinger equation are examined numerically. It is found that at forcing frequency above a critical value, f(c), only one solution exists. However, below f(c), multiple steady solutions, the number of which is determined, are possible. This multiplicity leads to hysteresis for f < f(c), in agreement with observation. A Hopf bifurcation of the steady solutions is found. This bifurcation is compared with the transition from unmodulated to periodically modulated cross-waves observed experimentally.
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Kwalik, Kristina Mary. "Bifurcation characteristics in closed-loop polymerization reactors." Diss., Georgia Institute of Technology, 1988. http://hdl.handle.net/1853/11711.
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Shen, Wenxian. "Staility and bifurcation of traveling wave solutions." Diss., Georgia Institute of Technology, 1992. http://hdl.handle.net/1853/29354.
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徐善強 and Sin-keung Chui. "Stability and bifurcation in flow induced vibration." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1997. http://hub.hku.hk/bib/B31235724.
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Chui, Sin-keung. "Stability and bifurcation in flow induced vibration /." Hong Kong : University of Hong Kong, 1997. http://sunzi.lib.hku.hk/hkuto/record.jsp?B1904155X.
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Brandon, Quentin. "Numerical method of bifurcation analysis for piecewise-smooth nonlinear dynamical systems." Toulouse, INSA, 2009. http://eprint.insa-toulouse.fr/archive/00000312/.
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Dans le domaine de l’analyse des systèmes dynamiques, les modèles lisses par morceaux ont gagné en popularité du fait de leur grande flexibilité et précision pour la représentation de certains systèmes dynamiques hybrides dans des applications telles que l’électronique ou la mécanique. Les systèmes dynamiques hybrides possèdent deux ensembles de variables, l’un évoluant dans un espace continu, l’autre dans un espace discret. La plupart des méthodes d’analyse nécessitent que l’orbite reste lisse pour être applicable, de telle sorte que certaines manipulations d’adaptation aux systèmes hybrides deviennent inévitables lors de leur analyse. Sur la base d’un modèle lisse par morceaux, où l’orbite du système est découpée en morceaux localement lisses, et une méthode d’analyse des bifurcations hybride, utilisant une application de Poincaré dont les sections sont régies par les conditions de commutation du système, nous étudions le processus d’analyse en détails. Nous analysons ensuite plusieurs extensions de l’oscillateur d’Aplazur, dont la version originale est un oscillateur bidimensionnel non-lisse à commutation. Ce dernier, en tant que système dynamique non linéaire à commutation, est un excellent candidat pour démontrer l’efficacité de cette approche. De plus, chaque extension présente un nouveau scénario, permettant d’introduire les démarches appropriées et d’illustrer la flexibilité du modèle. Finalement, afin d’exposer l’implémentation de notre programme, nous présentons quelques unes des méthodes numériques les plus pertinentes. Il est intéressant de signaler que nous avons choisi de mettre l’accent sur les systèmes dynamiques autonomes car le traitement des systèmes non-autonomes nécessitent seulement une simplification (pas de variation du temps). Cette étude présente une méthode généraliste et structurée pour l’analyse des bifurcations des systèmes dynamiques non-linéaires hybrides, illustrée par des résultats pratiques. Parmi ces derniers, nous exposons quelques propriétés locales et globales de l’oscillateur d’Alpazur, dont la présence d’une cascade de points cuspidaux dans le diagramme de bifurcation. Notre travail a abouti à la réalisation d’un outil d’analyse informatique, programmé en C++, utilisant les méthodes numériques que nous avons sélectionnées à cet effet, telles que l’approximation numérique de la dérivée seconde des éléments de la matrice JacobienneIn the field of dynamical system analysis, piecewise-smooth models have grown in popularity due to there greater flexibility and accuracy in representing some hybrid systems in applications such as electronics or mechanics. Hybrid dynamical systems have two sets of variables, one which evolve in a continuous space, and the other in a discrete one. Most analytical methods require the orbit to be smooth during objective intervals, so that some special treatments are inevitable to study the existence and stability of solutions in hybrid dynamical systems. Based on a piecewise-smooth model, where the orbit of the system is broken down into locally smooth pieces, and a hybrid bifurcation analysis method, using a Poincare map with sections ruled by the switching conditions of the system, we review the analysis process in details. Then we apply it to various extensions of the Alpazur oscillator, originally a nonsmooth 2-dimension switching oscillator. The original Alpazur oscillator, as a simple nonlinear switching system, was a perfect candidate to prove the efficiency of the approach. Each of its extensions shows a new scenario and how it can be handled, in order to illustrate the generality of the model. Finally, and in order to show more of the implementation we used for our own computer-based analysis tool, some of the most relevant numerical methods we used are introduced. It is noteworthy that the emphasis has been put on autonomous systems because the treatment of non-autonomous ones only requires a simplification (no time variation). This study brings a strong and general framework for the bifurcation analysis of nonlinear hybrid dynamical systems, illustrated by some results. Among them, some interesting local and global properties of the Alpazur Oscillator are revealed, such as the presence of a cascade of cusps in the bifurcation diagram. Our work resulted in the implementation of an analysis tool, implemented in C++, using the numerical methods that we chose for this particular purpose, such as the numerical approximation of the second derivative elements in the Jacobian matrix
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Aasen, Ailo. "A Study of Rotational Water Waves using Bifurcation Theory." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for fysikk, 2014. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-27092.
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This thesis is concerned with the water wave problem. Using local bifurcation we establish small-amplitude steady and periodic solutions of the Euler equations with vorticity. Our approach is based on that of Ehrnström, Escher and Wahlén \cite{EEW11}, the main difference being that we use new bifurcation parameters. The bifurcation is done both from a one-dimensional and a two-dimensional kernel, the latter bifurcation giving rise to waves having more than one crest in each minimal period. We also give a novel and rudimentary proof of a key lemma establishing the Fredholm property of the elliptic operator associated with the water wave problem. Furthermore, we investigate derivatives of the bifurcation curve, and present a new result for the corresponding linear problem.
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Sallam, M. H. M. "Aspects of stability and bifurcation theory for multiparameter problems." Thesis, University of Strathclyde, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.371969.
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Harrell, Maralee. "Chaos and reliable knowledge /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2000. http://wwwlib.umi.com/cr/ucsd/fullcit?p9987534.
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Ghosh, Archisman. "TIME-DEPENDENT SYSTEMS AND CHAOS IN STRING THEORY." UKnowledge, 2012. http://uknowledge.uky.edu/physastron_etds/9.
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One of the phenomenal results emerging from string theory is the AdS/CFT correspondence or gauge-gravity duality: In certain cases a theory of gravity is equivalent to a "dual" gauge theory, very similar to the one describing non-gravitational interactions of fundamental subatomic particles. A difficult problem on one side can be mapped to a simpler and solvable problem on the other side using this correspondence. Thus one of the theories can be understood better using the other.
The mapping between theories of gravity and gauge theories has led to new approaches to building models of particle physics from string theory. One of the important features to model is the phenomenon of confinement present in strong interaction of particle physics. This feature is not present in the gauge theory arising in the simplest of the examples of the duality. However this N = 4 supersymmetric Yang-Mills gauge theory enjoys the property of being integrable, i.e. it can be exactly solved in terms of conserved charges. It is expected that if a more realistic theory turns out to be integrable, solvability of the theory would lead to simple analytical expressions for quantities like masses of the hadrons in the theory. In this thesis we show that the existing models of confinement are all nonintegrable--such simple analytic expressions cannot be obtained.
We moreover show that these nonintegrable systems also exhibit features of chaotic dynamical systems, namely, sensitivity to initial conditions and a typical route of transition to chaos. We proceed to study the quantum mechanics of these systems and check whether their properties match those of chaotic quantum systems. Interestingly, the distribution of the spacing of meson excitations measured in the laboratory have been found to match with level-spacing distribution of typical quantum chaotic systems. We find agreement of this distribution with models of confining strong interactions, conforming these as viable models of particle physics arising from string theory.
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Klages, Rainer. "Deterministic chaos and diffusion: from theory to experiments." Diffusion fundamentals 2 (2005) 24, S. 1-2, 2005. https://ul.qucosa.de/id/qucosa%3A14354.
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Bullock, Mercedes. "Translating “Lunokhod”: Textual Order, Chaos and Relevance Theory." Thesis, Université d'Ottawa / University of Ottawa, 2020. http://hdl.handle.net/10393/40981.
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This thesis examines the concepts of textual order and chaos, and how Relevance Theory can be used to translate texts that do not adhere to conventional textual practices. Relevance Theory operates on the basis of presumed order in communication. Applying it to disordered communicative acts provides an opportunity and vocabulary to describe how communication can break down, and the consequences this can have for translation. This breakdown of order, which I am terming a ‘chaos principle’, will be examined through the lens of a Russian-language short story called “Lunokhod”, a story in which textual order, as described by Relevance Theory, breaks down.
In this thesis, I first lay out several translation challenges presented by my corpus, discuss each with reference to Relevance Theory, and examine the implications for translation through sample translation segments. This deconstruction section argues that conventional translation methods fail to properly address the challenges of my corpus. Next comes a reconstruction section, in which I develop a theoretical framework for my translation that has roots in Relevance Theory but that frees the translation from the constraints imposed by an ordered view of communication. Finally, I present the translation itself.
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Krcelic, Khristine M. "Chaos and Dynamical Systems." Youngstown State University / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=ysu1364545282.
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Charles, Guy Alexander. "Bifurcation tailoring applied to nonlinear flight dynamics." Thesis, University of Bristol, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.274630.
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Venkatagiri, Shankar C. "The peak-crossing bifurcation in lattice dynamical systems." Diss., Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/29340.
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Bengtsson, Jonas. "Thriving at the Edge of Chaos." Thesis, Blekinge Tekniska Högskola, Institutionen för programvaruteknik och datavetenskap, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:bth-5975.
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In this master thesis two different worldviews are compared: a mechanistic, and an organic worldview. The way we think the world and the nature work reflects on how we think organizations work, or how they ought to work. The mechanistic worldview has dominated our way of thinking since the seventeenth century, and it compares the world with a machine. The organic worldview could use a number of different metaphors, but the one addressed in this thesis is complexity theory. Complexity theory is related to chaos theory and is concerned with complex adaptive systems (cas). Complex adaptive systems exist everywhere and are systems such as the human immune system, economies, and ecosystems. What complexity theory tries to do is to understand these systems—how they arise, how they function and how order emerge in them. When looking at complex adaptive systems you can’t just look at the different parts. You must take a more holistic view and look at the whole and the interaction of the parts. If you just look at the parts you will miss the emergent properties that have emerged as the system has self-organized. One prominent aspect of these systems is that they don’t have any central authority, but somehow order do arise. In relation to organizations, complexity theory has something to say about almost all aspects of organizations: from what kind of leadership is needed, and how teams should be organized to the physical structure of the organization. To understand what complexity theory is and how to relate that to (software developing) organizations is the main focus of this thesis. Scrum is an agile and lightweight process which can be applied on development projects in general, but have been used in such diverse examples as software development projects, marketing programs, and business process reengineering (BPR) initiatives. In this thesis Scrum is used as an example of how to apply complexity theory to organizations. The result of the thesis showed that Scrum is highly influenced and compatible with complexity theory, which implies that complexity theory is of some use in software development. However, there are more work to be done to determine how effective it is, how to introduce it into organizations, and to explore more specific implementations. This master thesis should give the reader a good understanding of what complexity theory is, some specific issues to consider when applying complexity theory on organizations, and some specific examples of how to apply complexity theory on organizations.
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Monte, Brent M. "Chaos and the stock market." CSUSB ScholarWorks, 1994. https://scholarworks.lib.csusb.edu/etd-project/860.
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Snaith, Nina Claire. "Random matrix theory and zeta functions." Thesis, University of Bristol, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.322610.
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Pearce, S. P. "Bifurcation and stability of elastic membranes : theory and biological applications." Thesis, Keele University, 2010. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.518311.
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Bari, Rehana. "Local and global bifurcation theory for multiparameter nonlinear eigenvalue problems." Thesis, Heriot-Watt University, 1995. http://hdl.handle.net/10399/755.
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Harb, Ahmad M. "Application of Bifurcation Theory to Subsynchronous Resonance in Power Systems." Diss., Virginia Tech, 1996. http://hdl.handle.net/10919/30487.
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A bifurcation analysis is used to investigate the complex dynamics of two heavily loaded single-machine-infinite-busbar power systems modeling the characteristics of the BOARDMAN generator with respect to the rest of the North-Western American Power System and the CHOLLA# generator with respect to the SOWARO station. In the BOARDMAN system, we show that there are three Hopf bifurcations at practical compensation values, while in the CHOLLA#4 system, we show that there is only one Hopf bifurcation.
The results show that as the compensation level increases, the operating condition loses stability with a complex conjugate pair of eigenvalues of the Jacobian matrix crossing transversely from the left- to the right-half of the complex plane, signifying a Hopf bifurcation. As a result, the power system oscillates subsynchronously with a small limit-cycle attractor. As the compensation level increases, the limit cycle grows and then loses stability via a secondary Hopf bifurcation, resulting in the creation of a two-period quasiperiodic subsynchronous oscillation, a two-torus attractor. On further increases of the compensation level, the quasiperiodic attractor collides with its basin boundary, resulting in the destruction of the attractor and its basin boundary in a bluesky catastrophe. Consequently, there are no bounded motions.
When a damper winding is placed either along the q-axis, or d-axis, or both axes of the BOARDMAN system and the machine saturation is considered in the CHOLLA#4 system, the study shows that, there is only one Hopf bifurcation and it occurs at a much lower level of compensation, indicating that the damper windings and the machine saturation destabilize the system by inducing subsynchronous resonance.
Finally, we investigate the effect of linear and nonlinear controllers on mitigating subsynchronous resonance in the CHOLLA#4 system . The study shows that the linear controller increases the compensation level at which subsynchronous resonance occurs and the nonlinear controller does not affect the location and type of the Hopf bifurcation, but it reduces the amplitude of the limit cycle born as a result of the Hopf bifurcation.Ph. D.
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Correa, Alvaro. "Bifurcation theory for a class of second order differential equations." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/940.
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We consider positive solutions of the nonlinear two point boundary value problem u‘‘+λf(u)=0, u(-1)=u(1)=0 , f(u)=u(u-a)(u-b)(u-c)(1-u), 0, depending on a parameter λ. Each solution u(x) is even function, and it is uniquely identified by α=u(0). We will prove, using delicate integral estimates that α=b,1 are not bifurcations points. We explore and prove a series of properties which restrict the location of a bifurcation point by studying the change of concavity of the graph of f and the points where the rays from 0 and b touche the graph of f.
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Bi̇li̇r, Bülent. "Bifurcation analysis of nonlinear oscillations in power systems /." free to MU campus, to others for purchase, 2000. http://wwwlib.umi.com/cr/mo/fullcit?p9999273.
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Khůlová, Jitka. "Stabilita a chaos v nelineárních dynamických systémech." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2018. http://www.nusl.cz/ntk/nusl-392836.
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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.
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Genovese, Greg. "Does chaos theory have anything to do with literature? /." Title page, contents and introduction only, 1995. http://web4.library.adelaide.edu.au/theses/09AR/09arg3352.pdf.
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Smith, Andrew Peter. "Consumer's product choice behaviour : an application of chaos theory." Thesis, University of Stirling, 2000. http://hdl.handle.net/1893/1452.
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The primary aim of this thesis is to apply chaos theory to consumer behaviour research. Chaos theory is essentially a theory of time series. The specific focus is product choice consumption behaviour. The conceptual basis for the work is taken from a theory thus far developed entirely outwith the topic focus of consumer research and marketing. The concepts and methods developed by chaos theorists in the natural sciences and some social and behavioural sciences are synthesised with concepts and methods from consumer research. The objective is to both shed light on the consumption process and explore the potential of chaos theory in this field. Ultimately the work attempts to address the question of whether consumer behaviour can be 'chaotic' as described by chaos theory.In order to facilitate these objectives a diary study was conducted using sixty respondents. They were required to record their consumption of branded products for a period of three months. Five product categories were used with informants recording consumption of only one product type (twelve informants in each group). The product groups were as follows: soft drinks; savoury snacks; beer; chocolate snacks and packaged yoghurts and desserts. The data was coded and analysed by methods selected prior to data capture: weighted time series, spectral analysis and phase space analysis. One of the principal findings of the research was that distinctive forms of behaviour were identifiable within the data set as a whole from which a five-fold typology is proposed. However the complexity and individuality of the forms was marked despite this apparent typology. The spectral analysis shows little evidence of regular or periodic patterned behaviour; the series are essentially aperiodic. The phase space analysis reinforces and enhances the analysis of the weighted time series and suggests the series tend more towards chaos than ordered behaviour. The series obey certain 'rules' (i.e. they are 'randomised' but not random) consistent with the existence of determnistic chaos. Moreover they appear globally stable and locally unstable. These findings have a number of implications for various areas of consumer research (e.g. varety seeking, loyalty and other aspects of consumption) and successfully extend the application of chaos theory to another area of human behaviour research.