Dissertations / Theses on the topic 'Chaos map'
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1
Barton, Nicholas. "Transport and spectral properties of the one dimensional sine map." Thesis, University of Warwick, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.269050.
2
Cartwright, Julyan H. E. "Chaos in dissipative systems : bifurcations and basins." Thesis, Queen Mary, University of London, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.313920.
3
Švihálková, Kateřina. "Stabilizace chaosu: metody a aplikace." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2016. http://www.nusl.cz/ntk/nusl-254422.
Abstract:
The diploma thesis is focused on the use of heuristic and metaheuristic methods to stabilization and controlling the selected systems distinguished by the deterministic chaos behavior. There are discussed parameterization of chosen optimization methods, which are the genetic algorithm, simulated annealing and pattern search. The thesis also introduced the suitable controlling methods and the definition of the objective function. In the theoretical part of the thesis there is a brief introduction to the deterministic chaos theory. The next chapters describes the most common and deployed methods in~the~control theory, especially OGY and Pyragas methods. The practical part of the thesis is divided into two chapters. The first one describes the~stabilization of the artifical chaotic systems with the time delayed Pyragas method - TDAS and its modification ETDAS. The second chapter shows the real chaotic system control. The Duffing oscillator system was chosen to serve this purpose.
4
Guo, Yu. "BIFURCATION AND CHAOS OF NONLINEAR VIBRO-IMPACT SYSTEMS." OpenSIUC, 2013. https://opensiuc.lib.siu.edu/dissertations/725.
Abstract:
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.
5
Taylor, Imogen T. F. "Control and synchronisation of coupled map lattices : interdisciplinary modelling of synchronised dynamic behaviour (insects in particular)." Thesis, University of Derby, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275687.
6
Lippolis, Domenico. "How well can one resolve the state space of a chaotic map?" Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/33841.
Abstract:
All physical systems are affected by some noise that limits the resolution that can be attained in partitioning their state space. For chaotic, locally hyperbolic flows, this resolution depends on the interplay of the local stretching/contraction and the smearing due to noise. My goal is to determine the `finest attainable' partition for a given hyperbolic dynamical system and a given weak additive
white noise. That is achieved by computing the local eigenfunctions of the Fokker-Planck evolution operator in linearized neighborhoods of the periodic orbits of the corresponding deterministic system, and using overlaps of
their widths as the criterion for an optimal partition. The Fokker-Planck evolution is then represented by a finite transition graph, whose spectral determinant yields time averages of dynamical observables. The method applies in
principle to both continuous- and discrete-time dynamical systems. Numerical tests of such optimal partitions on unimodal maps support my hypothesis.
7
Courtot, Ariane. "Réviser les pluies de météores : caractérisation du chaos dans les courants de météoroïdes." Electronic Thesis or Diss., Université Paris sciences et lettres, 2023. http://www.theses.fr/2023UPSLO007.
Abstract:
Un courant de météoroïdes est formé lorsque des météoroïdes sont éjectés par un corps parent (astéroïde ou comète). Lorsque ce courant rencontre la Terre, une pluie de météores apparaît. Ce lien entre météores observés et corps parent est difficile à établir, à cause notamment de la dynamique complexe des météoroïdes (forces non-gravitationelles -FNGs- et rencontres proches). Je définis donc un "groupe de météores" comme un ensemble de météores aux caractéristiques proches, mais dont le lien avec le corps parent est incertain. J'ai passé en revue les méthodes utilisées pour former des groupes: critère de dissimilarité des orbites et algorithmes de groupement. Au vu des incomplétudes remarquées, j'ai choisi de m'intéresser à ce problème sous l'angle du chaos, défini comme l'augmentation exponentielle de la distance entre deux orbites initialement infiniment proches. J'ai sélectionné un indicateur de chaos adapté, puis j'ai réalisé des cartes de chaos sur les Géminides, les Draconides et les Léonides, trois pluies de météores aux orbites très différentes. On montre comment les résonances de moyen mouvement (RMMs) capturent les particules et les empêchent de rencontrer la planète responsable de la RMM. Cet effet est plus important dans le cas de RMMs plus larges. Cependant, les FNGs peuvent modifier cet effet. Pour les Géminides, il existe un rayon limite en-dessous duquel la diffusion due aux FNGs empêche la capture dans les RMMs. En revanche, pour les Draconides et les Léonides, ce rayon limite est bien plus faible, et n'est pas atteint dans mes simulations. Cela est dû à la fois à la largeur des RMMs, bien supérieure à celle des Géminides, et l'effet plus faible des FNGs à masse égale par rapport aux Géminides. Enfin, je me suis intéressée aux Taurides, pour lesquelles le lien avec le corps parent fait l'objet de recherches, et plus particulièrement aux branches Nord et Sud. Cette fois, j'ai choisi d'utiliser les observations des météores. Elles se sont révélées difficiles à exploiter pour une étude dynamique et j'ai donc dû sélectionner moi-même des particules qui correspondent aux Taurides (selon leur position dans le ciel et leur vitesse au moment de leur rencontre avec la Terre). Les cartes montrent le chaos très élevé des Taurides et l’absence du mécanisme lié aux RMMs. Ces différences pourraient justifier la classification des Taurides en groupe plutôt qu'en pluie. J'ai eu des difficultés à retrouver les Taurides Sud dans mes données, ce qui jette un doute sur la validité de cette branche. D'autres intégrations sont nécessaires pour investiguer ces résultats, mais les cartes de chaos donnent de premières indications sur la différence groupe/pluieA meteoroid stream is formed when meteoroids are ejected by a parent body (asteroid or comet). When this stream encounters the Earth, a meteor shower appears. This link between observed meteors and their parent body is difficult to establish, mainly because of the complex dynamics of meteoroids (non-gravitational forces -NGFs- and close encounters). I therefore define a 'meteor group' as a set of meteors with similar characteristics, but whose link with the parent body is uncertain.I have reviewed the methods used to form groups: orbit dissimilarity criteria and grouping algorithms. In view of the incompleteness observed, I chose to look at this problem from the angle of chaos, defined as the exponential increase in the distance between two orbits that are initially infinitely close.I selected a suitable chaos indicator and then produced chaos maps of the Geminids, Draconids and Leonids, three meteor showers with very different orbits. I showed how mean motion resonances (MMRs) capture the particles and prevent them from encountering the planet responsible for the MMR. This effect is greater in the case of larger MMRs.However, NGFs can modify this effect. For Geminids, there is a limiting radius below which diffusion due to NGFs prevents capture in MMRs. On the other hand, for Draconids and Leonids, this limiting radius is much smaller, and is not reached in my simulations. This is due both to the width of the RMMs, which is much greater than that of the Geminids, and to the weak effect of the NGFs for the same mass for these orbits, unlike the Geminids.Finally, I turned my attention to the Taurids, for which the link with the parent body is the topic of several studies, and more particularly to the North and South branches. This time, I chose to use meteor observations. These proved difficult to exploit for a dynamic study, so I had to select the particles that corresponded to the Taurids myself (according to their position in the sky and their speed at the time of their encounter with the Earth).The maps show the very high chaos of the Taurids and the absence of the MMR mechanism. These differences could justify classifying the Taurids as a group rather than a shower. I had difficulty finding the Southern Taurids in my data, which casts doubt on the validity of this branch. Further integrations are needed to investigate these results, but the chaos maps give some initial indications of the group/shower distinction
8
Rollin, Guillaume. "Chaos dynamique dans le problème à trois corps restreint." Thesis, Besançon, 2015. http://www.theses.fr/2015BESA2028/document.
Abstract:
Capture-évolution-éjection de particules par des systèmes binaires (étoile-planète, étoile binaire, étoile-trou noir supermassif, trou noir binaire, ...). Dans une première partie, en utilisant une généralisation de l'application de Kepler, nous décrivons, au travers du cas de 1P/Halley, la dynamique chaotique des comètes dans le système solaire. Le système binaire, alors considéré, est composé du Soleil et de Jupiter. L'application symplectique utilisée permet de rendre compte des différentes caractéristiques de la dynamique : trajectoires chaotiques, îlots invariants de KAM associés aux résonances avec le mouvement orbital de Jupiter,... Nous avons déterminé de façon exacte et semi-analytique l'énergie échangée (fonction kick) entre le système solaire et la comète de Halley à chaque passage au périhélie. Cette fonction kick est la somme des contributions des problèmes à trois corps Soleil-planète-comète associés aux 8 planètes du système solaire. Nous avons montré que chacune de ces contributions peut être décomposée en un terme keplerien associé au potentiel gravitationnel de la planète et un terme dipolaire dû au mouvement du soleil autour du centre de masse du système solaire. Dans une deuxième partie, nous avons utilisé la généralisation de l'application de Kepler pour étudier la capture de particules de matière noire au sein des systèmes binaires. La section efficace de capture a été calculée et montre que la capture à longue portée est bien plus efficace que la capture due aux rencontres proches. Nous montrons également l'importance de la vitesse de rotation du système binaire dans le processus de capture. Notamment, un système binaire en rotation ultrarapide accumulera en son sein une densité de matière jusqu'à 10^4 fois celle du flot de matière le traversant. Dans la dernière partie, en intégrant les équations du mouvement du problème à trois corps restreint plan, nous avons étudié l'éjection des particules capturées par un système binaire. Dans le cas d'un système binaire dont les deux corps sont de masses comparables, alors que la majorité des particules sont éjectées immédiatement, nous montrons, sur les sections de Poincaré, que la trace des particules restant indéfiniment aux abords du système binaire forme une structure fractale caractéristique d'un répulseur étrange associé à un système chaotique ouvert. Cette structure fractale, également présente dans l'espace réel, a une forme de spirale à deux bras partageant des similitudes avec les structures spiralées des galaxies comme la nôtreThis work is devoted to the study of the restricted 3-body problem and particularly to the capture-evolution-ejection process of particles by binary systems (star-planet, binary star, star-supermassive black hole, binary black hole, ...). First, using a generalized Kepler map, we describe, through the case of 1P/Halley, the chaotic dynamics of comets in the Solar System. The here considered binary system is the couple Sun-Jupiter. The symplectic application we use allows us to depict the main characteristics of the dynamics: chaotic trajectories, KAM islands associated to resonances with Jupiter orbital motion, ... We determine exactly and semi-analytically the exchange of energy (kick function) between the Solar System and 1P/Halley at its passage at perihelion. This kick function is the sum of the contributions of 3-body problems Sun-planet-comet associated to the eight planets. We show that each one of these contributions can be split in a keplerian term associated to the planet gravitational potential and a dipolar term due to the Sun movement around Solar System center of mass. We also use the generalized Kepler map to study the capture of dark matter particles by binary systems. We derive the capture cross section showing that long range capture is far more efficient than close encounter induced capture. We show the importance of the rotation velocity of the binary in the capture process. Particularly, a binary system with an ultrafast rotation velocity accumulates a density of captured matter up to 10^4 times the density of the incoming flow of matter. Finally, by direct integration of the planar restricted 3-body problem equations of motion, we study the ejection of particles initially captured by a binary system. In the case of a binary with two components of comparable masses, although almost all the particles are immediately ejected, we show, on Poincaré sections, that the trace of remaining particles in the vicinity of the binary form a fractal structure associated to a strange repeller associated to chaotic open systems. This fractal structure, also present in real space, has a shape of two arm spiral sharing similarities with spiral structures observed in galaxies such as the Milky Way
9
Krützmann, Nikolai Christian. "Application of Complexity Measures to Stratospheric Dynamics." Thesis, University of Canterbury. Physics and Astronomy, 2008. http://hdl.handle.net/10092/2020.
Abstract:
This thesis examines the utility of mathematical complexity measures for the analysis of stratospheric dynamics. Through theoretical considerations and tests with artificial data sets, e.g., the iteration of the logistic map, suitable parameters are determined for the application of the statistical entropy measures sample entropy (SE) and Rényi entropy (RE) to methane (a long-lived stratospheric tracer) data from simulations of the SOCOL chemistry-climate model. The SE is shown to be useful for quantifying the variability of recurring patterns in a time series and is able to identify tropical patterns similar to those reported by previous studies of the ``tropical pipe'' region. However, the SE is found to be unsuitable for use in polar regions, due to the non-stationarity of the methane data at extra-tropical latitudes. It is concluded that the SE cannot be used to analyse climate complexity on a global scale. The focus is turned to the RE, which is a complexity measure of probability distribution functions (PDFs). Using the second order RE and a normalisation factor, zonal PDFs of ten consecutive days of methane data are created with a Bayesian optimal binning technique. From these, the RE is calculated for every day (moving 10-day window). The results indicate that the RE is a promising tool for identifying stratospheric mixing barriers. In Southern Hemisphere winter and early spring, RE produces patterns similar to those found in other studies of stratospheric mixing. High values of RE are found to be indicative of the strong fluctuations in tracer distributions associated with relatively unmixed air in general, and with gradients in the vicinity of mixing barriers, in particular. Lower values suggest more thoroughly mixed air masses. The analysis is extended to eleven years of model data. Realistic inter-annual variability of some of the RE structures is observed, particularly in the Southern Hemisphere. By calculating a climatological mean of the RE for this period, additional mixing patterns are identified in the Northern Hemisphere. The validity of the RE analysis and its interpretation is underlined by showing that qualitatively similar patterns can be seen when using observational satellite data of a different tracer. Compared to previous techniques, the RE has the advantage that it requires significantly less computational effort, as it can be used to derive dynamical information from model or measurement tracer data without relying on any additional input such as wind fields. The results presented in this thesis strongly suggest that the RE is a useful new metric for analysing stratospheric mixing and its variability from climate model data. Furthermore, it is shown that the RE measure is very robust with respect to data gaps, which makes it ideal for application to observations. Hence, using the RE for comparing observations of tracer distributions with those from model simulations potentially presents a novel approach for analysing mixing in the stratosphere.
10
Weirauch, Angelika. "Kreativität – wie man Sinn und Freude im Chaos der Existenz findet." Master's thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2013. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-115571.
Abstract:
Die Arbeit befasst sich mit unterschiedlichen philosophischen, psychologischen und erziehungswissenschaftlichen Ansätzen der Kreativitätsforschung und mit einem Selbstversuch. Eine These ist, dass veränderte Bewusstseinszustände (wie z.B. Schlaf, Rausch, Krankheit aber auch körperliche Ausarbeitung wie das Wandern) besondere Zugänge zur Kreativität sind.
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Feltekh, Kais. "Analyse spectrale des signaux chaotiques." Phd thesis, INSA de Toulouse, 2014. http://tel.archives-ouvertes.fr/tel-01071919.
Abstract:
Au cours des deux dernières décennies, les signaux chaotiques ont été de plus en plus pris en compte dans les télécommunications, traitement du signal ou transmissions sécurisées. De nombreux articles ont été publiés qui étudient la densité spectrale de puissance (DSP) des signaux générés par des transformations spécifiques. La concentration sur la DSP est due à l'importance de la fréquence dans les télécommunications et la transmission sécurisée. Grâce au grand nombre de systèmes sans fil, la disponibilité des fréquences de transmission et de réception est de plus en plus rare pour les communications sans fil. Aussi, les médias guidés ont des limitations liées à la bande passante du signal. Dans cette thèse, nous étudions certaines propriétés associées à la bifurcation collision de frontière pour une transformation unidimensionnelle linéaire par morceaux avec trois pentes et deux paramètres. Nous calculons les expressions analytiques de l'autocorrélation et de la densité spectrale de puissance des signaux chaotiques générés par les transformations linéaires par morceaux. Nous montrons l'existence d'une forte relation entre les différents types de densité spectrale de puissance (passe-bas, passe-haut ou coupe-bande) et les paramètres de bifurcation. Nous notons également en évidence une relation entre le type de spectre et l'ordre des cycles attractifs. Le type du spectre dépend de l'existence des orbites périodiques au-delà de la bifurcation de collision de frontière qui a donné naissance au chaos. Nous utilisons ensuite les transformations chaotiques pour étudier la fonction d'ambiguïté. Nous combinons quelques transformations chaotiques bien déterminées pour obtenir un spectre large bande avec une bonne fonction d'ambiguïté qui peut être utilisée en système radar.
12
Minář, Petr. "Nelineární řízení komplexních soustav s využitím evolučních přístupů." Doctoral thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2018. http://www.nusl.cz/ntk/nusl-364594.
Abstract:
Control theory of complex systems by utilization of artificial intelligent algorithms is relatively new science field and it can be used in many areas of technical practise. Best known algorithms to solved similar tasks are genetic algorithm, differential evolution, HC12 Nelder-Mead method, fuzzy logic and grammatical evolution. Complex solution is presented at selected examples from mathematical nonlinear systems to examples of anthems design and stabilization of deterministic chaos. The goal of this thesis is present examples of implementation and utilization of artificial algorithms by multi-objective optimization. To achieve optimal results is used designed software solution by multi-platform application, which used Matlab and Java interfaces. The software solution integrate every algorithms of this thesis to complex solution and it extends possible application of those approaches to real systems and practical world.
13
Jeon, Seung-Hwa. "L'inexplicable chez Samuel Beckett : Dieux du chaos et monstres inconcevables." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC127/document.
Abstract:
Le but de cette recherche est de montrer comment s’effondrent les clichés et comment existe l’inexplicable, qui est, selon Beckett, une des conditions de l’existence avec la lumière et l’obscurité, et qui est aussi le chaos composé par l’art détruisant préjugés et clichés, aperçu par Gilles Deleuze et Félix Guattari. Cette démonstration se propose donc, d’une part, d’examiner la chute des dieux de la création, sources de la vérité, de la sagesse et du progrès, et leur dénaturation en dieux du chaos, et d’autre part, les éléments anormaux de l’écriture, susceptibles d’être nommés monstres, en raison de leur étrangeté et de leur ambiguïté qui empêchent de les définir. Pour ce qui concerne les dieux du chaos, il s’agit de la parodie du Dieu chrétien, de Jésus-Christ et de Prométhée l’inventeur, et de leur dégradation aboutissant à ce que le créateur ne se distingue plus de sa créature. Quant aux monstres inconcevables, leurs conditions et les réactions négatives envers eux, qui sous-entendent paradoxalement la monstrualisation, sont révélées par le thème des fleurs, et deux images mythiques, androgynes et siamoises, dévoilent l’impossibilité de l’identification ou de la signifiance, et l’état de l’entre-deux ou de la confusionThe purpose of this thesis is to show how clichés collapse and exists the inexplicable that Beckett notices as a condition of existence that coexists with other conditions, light and darkness ; and as chaos, composed by art destroying prejudices and clichés, and seen by Gilles Deleuze and Félix Guattari. This demonstration therefore proposes, on the one hand, to examine the fall of the gods of creation, sources of truth, wisdom and progress, and their denaturation into gods of chaos, and on the other hand, the elements abnormal writing, likely to be named monsters, because of their strangeness and ambiguity that prevent them from being defined. As for the gods of chaos, it will be the parody of the Christian God, Jesus Christ and Prometheus the inventor, and their degradation by which the creator will no longer be distinguished from his creature. As for the inconceivable monsters, the conditions of the monsters and the negative reactions towards them, which paradoxically imply the monstrualization, will be revealed by the theme of flowers, and the two mythical images, androgynous and Siamese, will reveal the impossibility of the identification or the significance, and the state of the interstage or confusion
14
CARMO, Ricardo Batista do. "Um mapa discreto unidimensional para o sistema de Rössler." Universidade Federal de Pernambuco, 2015. https://repositorio.ufpe.br/handle/123456789/18322.
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Dissertação - Ricardo Batista.pdf: 10061311 bytes, checksum: ce7d296a73fc33cb8f4605b5e94a9cfb (MD5)Made available in DSpace on 2017-02-15T12:52:08Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertação - Ricardo Batista.pdf: 10061311 bytes, checksum: ce7d296a73fc33cb8f4605b5e94a9cfb (MD5) Previous issue date: 2015-03-02
CNPq
Centros de periodicidade e caos (CPCs) s˜ao pontos que podem aparecer quando projetamos certo expoente de Lyapunov λ em um plano de parˆametros de um sistema dinˆamico dissipativo. Espirais de solu¸c˜oes peri´odicas (λ < 0) e ca´oticas (λ > 0) circulam alternadamente um CPC, como aquele no ter¸co inferior direito na figura da folha de rosto. Nesta disserta¸c˜ao foi desenvolvido inicialmente um programa para o c´alculo num´erico do espectro de Lyapunov de um sistema dinˆamico tridimensional (3D) gen´erico. Em seguida, CPCs foram procurados e achados nas solu¸c˜oes das equa¸c˜oes de R¨ossler, que possuem trˆes parˆametros, a, b, e c. Em particular, para b = bc = 0.17872, o CPC foi encontrado no plano a×c com coordenadas a = ac = 0.17694 e c = cc = 10.5706. Fixando a = ac e tomando c como um parˆametro de controle no intervalo 3 < c < cc, uma sequˆencia de dobramentos de per´ıodo seguida por uma sequˆencia de janelas de adi¸c˜ao de per´ıodo dentro da regi˜ao ca´otica. Ajustes por fun¸c˜oes simples de mapas de retorno de m´aximos locais em uma das vari´aveis dinˆamicas do sistema de R¨ossler permitiram a elabora¸c˜ao de um mapa discreto unidimensional Mr(x) no intervalo unit´ario, o qual faz a m´ımica sin´optica da dinˆamica do fluxo. A raz˜ao de convergˆencia para a sequˆencia de adi¸c˜ao de per´ıodo foi estimada dos ciclos superest´aveis do mapa como um valor pouco acima de 1.7, em bom acordo com o que se obt´em do sistema de R¨ossler. Uma f´ormula para a medida invariante foi obtida de um ajuste para a distribui¸c˜ao das iteradas em regime erg´odico. O correspondente expoente de Lyapunov, 0.597, est´a em bom acordo com 0.588, valor obtido da m´edia discreta de ln|Mr(xi)|.
Aperiodicityhub(PH)isthecommoncenterofperiodic(λ < 0)andchaotic(λ > 0) spirals which show up when a characteristic Lyapunov exponent λ of a dissipative dynamical system is projected onto a planar subset of its parameter space. The color plate in a previous page of this document shows one such PH in the lower right third. In this work Lyapunov spectra of three-dimensional dynamical systems were numericallycalculatedwithastandardalgorithmwhichreliesonrepeatedapplication of the Gram-Schmidt orghonormalization procedure on certain vectors in the phase space. PHs were then searched and found in the R¨ossler system, which has three parameters, namely, a,b, and c. In particular, for b = bh = 0.17872, a PH was found in the ca-plane with coordinates a = ah = 0.17694 and c = ch = 10.5706. By fixing a = ah and taking c as a control parameter in the interval 3 < c < ch, a complete sequence , i.e., a period-doubling sequence followed by a sequence of period-adding windows within the chaotic region, was observed. Fits to tens of return maps for local maxima in one of the dynamical variables allowed the construction of a oneparameter one-dimensional discrete map in the unit interval that synoptically mimics the dynamics of the flow. The convergence ratio for the period-adding sequence was estimated from the superstable cycles as 1.7, in good agreement with the value obtained from the R¨ossler system. At full ergodicity, a formula for the invariant measurewasobtainedfromafittothedistributionoftheiterates. Fromthatformula, we estimated a Lyapunov exponent of 0.597, which is in reasonable agreement with 0.588, the value obtained straightforwardly from the discrete iterates of the map.
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Zaïbi, Ghada. "Sécurisation par dynamiques chaotiques des réseaux locaux sans fil au niveau de la couche MAC." Phd thesis, Toulouse 2, 2012. http://tel.archives-ouvertes.fr/tel-00867469.
Abstract:
Les travaux de recherche de cette thèse s'inscrivent dans le cadre de la sécurité par chaos des réseaux locaux sans fil, en particulier les réseaux de capteurs sans fil. L'originalité de cette thèse consiste à proposer des cryptosystèmes à base de chaos plus adaptés aux réseaux de capteurs, en termes de consommation d'énergie, que les algorithmes conventionnels et à réaliser une implémentation sur une plateforme réelle. Nous présentons en premier lieu un état de l'art des réseaux, les menaces, les contraintes limitant le processus de sécurité des informations ainsi que les principales techniques de cryptographie. Nous donnons un aperçu sur la théorie de chaos et nous validons l'aspect aléatoire de plusieurs suites chaotiques par les tests statistiques du NIST. Nous proposons ensuite des nouvelles méthodes de construction de S-Box chaotiques tout en prouvant leur robustesse contre les attaques traditionnelles. Nous proposons enfin un nouvel algorithme de cryptage d'image dédié au réseau de capteurs sans fil. La validation de nos contributions est effectuée par simulation et par des mesures expérimentales sur une plateforme de réseaux de capteurs réels (SensLab).
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Moisan, Marcelo. "Synthèse d'observateurs par intervalles pour des systèmes biologiques mal connus." Nice, 2007. http://www.theses.fr/2007NICE4059.
Abstract:
Cette thèse présente de nouveaux résultats sur l'estimation robuste d'état, avec des applications aux systèmes biologiques représentés par des modèles approximatifs. Les modèles mathématiques en biologie sont connus pour être fortement incertains. Nous développons des observateurs par intervalles, basés sur la théorie de systèmes différentiels positifs. L'objectif d'un observateur par intervalles est d'obtenir des bornes supérieures et inférieures garanties pour les variables non mesurées du système. Ceci est réalisé en considérant que des bornes sur les incertitudes sont connues. Le principe des observateurs que nous développons repose sur un faisceau d'estimateurs par intervalle : nous lançons en parallèle plusieurs estimations par intervalles, puis nous en prenons l'enveloppe supérieure et inférieure pour obtenir l'estimation finale. Nous étendons tout d'abord les résultats existants aux systèmes non monotones. Nous proposons ensuite une stratégie pour localiser les gains optimaux pour le faisceau d'observateur. Nous améliorons également les estimations en construisant des observateurs pour le système en temps inversé. Enfin ces principes sont étendus a l'estimation des entrées inconnues. Les observateurs par intervalles offrent de nombreux avantages en comparaison aux méthodes classiques d'estimation d'état. Tout d'abord ils permettent de gérer l'incertitude dans un cadre déterministe. Ils peuvent être comparés à d'autres estimations par intervalles, et finalement être améliorés en prenant l'intersection des prédictions. En outre, il est possible d'évaluer en ligne la performance de l'estimateur en suivant la largeur de l'intervalle prédit. Les contributions présentées dans cette thèse sont illustrées par des applications à divers bioprocédés, notamment en utilisant des modèles de croissance de microorganismes sur un substrat. Des essais sur un procédé industriel d'épuration de l'eau valident ces observateurs dans un cadre réel. Finalement des applications à des systèmes chaotiques sont également étudiéesThis thesis presents new results in the field of robust state estimation, with applications to uncertain biotechnological systems. Mathematical models in biology are known to be highly uncertain. Therefore, we develop interval observers, based on the theory of positive differential systems. The objective of an interval observer is to obtain guaranteed upper and lower bounds for the unmeasured variables of the system. This is achieved considering that bounds on the uncertainties are known. Our observer design is featured by the so-called bundle of observers: we run in parallel several interval estimates and then we take the best inner envelope. We design interval observers for non-monotone systems. We develop an optimality criterion associated to interval observers, allowing to find the optimal gains for an observers bundle. We construct reverse time interval observers in order to improve convergence rate and we extend these principles to the estimation of unknown inputs. Some of the main advantages of interval observers are that they offer a way to manage uncertainty, considering a deterministic framework. They can be compared with other guaranteed state estimation methods, allowing improvements when taking the intersection of the predictions. They also allow to online assess the convergence of the estimates. The contributions presented in this thesis are illustrated through their application to biotechnological systems, namely in models of microorganism consuming one substrate. The application to a real industrial wastewater treatment plant let us validate the proposed methods. Finally, we also studied applications to the estimation of uncertain chaotic systems
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Al-saedi, Mohammed Abdullah. "Examination of Acousto-Optic Chaos and Application to RF Signal Encryption and Recovery." University of Dayton / OhioLINK, 2012. http://rave.ohiolink.edu/etdc/view?acc_num=dayton1337808954.
18
Sendrowski, Janek. "Feigenbaum Scaling." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-96635.
Abstract:
In this thesis I hope to provide a clear and concise introduction to Feigenbaum scaling accessible to undergraduate students. This is accompanied by a description of how to obtain numerical results by various means. A more intricate approach drawing from renormalization theory as well as a short consideration of some of the topological properties will also be presented. I was furthermore trying to put great emphasis on diagrams throughout the text to make the contents more comprehensible and intuitive.
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Hruboš, Zdeněk. "Oscilátory generující nekonvenční signály." Doctoral thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2016. http://www.nusl.cz/ntk/nusl-239937.
Abstract:
Dizertační práce se zabývá elektronicky nastavitelnými oscilátory, studiem nelineárních vlastností spojených s použitými aktivními prvky a posouzením možnosti vzniku chaotického signálu v harmonických oscilátorech. Jednotlivé příklady vzniku podivných atraktorů jsou detailně diskutovány. V doktorské práci je dále prezentováno modelování reálných fyzikálních a biologických systémů vykazujících chaotické chování pomocí analogových elektronických obvodů a moderních aktivních prvků (OTA, MO-OTA, CCII ±, DVCC ±, atd.), včetně experimentálního ověření navržených struktur. Další část práce se zabývá možnostmi v oblasti analogově – digitální syntézy nelineárních dynamických systémů, studiem změny matematických modelů a odpovídajícím řešením. Na závěr je uvedena analýza vlivu a dopadu parazitních vlastností aktivních prvků z hlediska kvalitativních změn v globálním dynamickém chování jednotlivých systémů s možností zániku chaosu v důsledku parazitních vlastností použitých aktivních prvků.
20
Blank, Iréne, and Magdalena Fridén. "“Man kan ju inte vara kunnig innan man fått en chans att lära sig” : En studie om byggbranschens upplevelser av yrkeselevers yrkeskunnande." Thesis, Stockholms universitet, Institutionen för pedagogik och didaktik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-144509.
Abstract:
Syftet med denna studie är att undersöka hur praktikhandledare inom bygg- och anläggningsprogrammet uppfattar byggelevers yrkeskunnande och om de upplever någon skillnad i yrkeskunnandet mot före gymnasiereformen 2011. Studie- och yrkesvägledare fungerar som en länk mellan eleverna och branscherna där det är viktigt för vägledaren att ha kännedom om branschernas synsätt. Studien är genomförd med kvalitativ metod där tio APL-handledare på byggarbetsplatser i Värmlands län intervjuats. Intervjuerna är analyserade enligt innehållsanalys och ställs mot Illeris teorier om lärande och kompetens. Analyserna är inramade av Bourdieus habitusteori. Resultaten visar att APL-handledare har svårt att definiera vad yrkeskunnande är och därmed har uppfattningarna skiljts åt gällande vad som förväntas av APL-elever. Det framkommer även att egenskaper som förväntas av APL-eleverna närmast kan definieras som Bourdieus kapital än konkreta yrkesfärdigheter. Våra resultat visar dessutom att APL-handledarna inte har någon uppfattning om vad som står i examensmålen för bygg- och anläggningsprogrammet. Vi hoppas att denna studie ska bidra till en ökad förståelse för studie- och yrkesvägledarens uppdrag som ibland blir en medlande länk mellan de olika aktörerna; skolan, arbetslivet och eleven.The purpose of this study is to investigate what building and construction workers who mentor students from the vocational-education program of building and construction think about the students’ vocational skills. The study also hope to ascertain whether the construction workers have noticed any difference in the students’ vocational skills after the school reform of 2011. As aspiring guidance counsellors we aim to play the role of a bridge between the students and their chosen field of employment. For guidance counsellors it is important to have a solid grasp of the values and views found in different fields of employment and to manage the expectations of the students. For this study, we used a qualitative method in which we interviewed ten mentors on construction sites across the county of Wermland. The content of the interviews was later analysed and compared to Illeris’ theory of knowledge and competence. As a theoretical framework, we also used Bourdieu’s theory of Habitus. The results show that the mentors had difficulty defining vocational skills in a meaningful and concise manner, which leads to students finding it difficult to know what is expected of them. The characteristics of the students are better defined in Bourdieu’s theory of habitus. The results also revealed that the mentors did not have a clear picture of what was expected of a student and did not understand fully what the student would need to learn in order to pass the relevant examinations at the end of the course. We hope that this study will contribute to a clearer understanding of the role of the guidance counsellor, which in this case is to act as a bridge between those already working in the construction industry and the students hoping to work within the construction industry after they have graduated.
21
Беляев, А. В., and A. V. Belyaev. "Анализ стохастических моделей живых систем с дискретным временем : магистерская диссертация." Master's thesis, б. и, 2020. http://hdl.handle.net/10995/87578.
Abstract:
Работа содержит исследования трех моделей живых систем с дискретным временем. В первой главе рассматривается одномерная модель нейронной активности, задаваемая кусочно-гладким отображением. Показывается, что в случае одномерного отображения наличие случайного возмущения приводит к появлению всплесков (спайкингу). Исследуются два механизма генерации спайков, вызванных добавлением случайного возмущения в один из параметров. Иллюстрируется, что сосуществование двух аттракторов является не единственной причиной возникновения спайкинга. Для прогнозирования уровня интенсивности шума, необходимого для генерации спайков, применяется метод доверительных областей, который основан на функции стохастической чувствительности. Также находятся основные характеристики межспайковых интервалов в зависимости от интенсивности шума. Вторая глава работы посвящена применению метода функции стохастической чувствительности к аттракторам кусочно-гладкого одномерного отображения, описывающего динамику численности популяции. Первым этапом исследования является параметрический анализ возможных режимов детерминированной модели: определение зон существования устойчивых равновесий и хаотических аттракторов. Для определения параметрических границ хаотического аттрактора применяется теория критических точек. В случае, когда на систему оказывает влияние случайное воздействие, на основе техники функции стохастической чувствительности дается описание разброса случайных состояний вокруг равновесия и хаотического аттрактора. Проводится сравнительный анализ влияния параметрического и аддитивного шума на аттракторы системы. С помощью техники доверительных интервалов изучаются вероятностные механизмы вымирания популяции под действием шума. Анализируются изменения параметрических границ существования популяции под действием случайного возмущения. В третьей главе проводится анализ возможных динамических режимов детерминированной и стохастической модели Лотки-Вольтерры. В зависимости от двух параметров системы строится карта режимов. Изучаются параметрические зоны существования устойчивых равновесий, циклов, замкнутых инвариантных кривых, а также хаотических аттракторов. Описываются бифуркации удвоения периода, Неймарка--Саккера и кризиса. Демонстрируется сложная форма бассейнов притяжения. Помимо детерминированной системы подробно изучается стохастическая, описывающая влияние внешнего случайного воздействия. В случае хаоса дан алгоритм нахождения критических линий, описывающих границу хаотического аттрактора. Опираясь на найденную чувствительность аттракторов, строятся доверительные полосы и эллипсы, позволяющие описать разброс случайных состояний вокруг детерминированного аттрактора.The work contains study of three models of biological systems with discrete time. In the first chapter a one-dimensional model of neural activity defined by a piecewise-smooth map is considered. It is shown that in the case of a one-dimensional model, the presence of a random disturbance leads to a spike generation. Two mechanisms of spike generation caused by the presence of a random disturbance in one of the parameters are investigated. It is illustrated that the coexistence of two attractors is not the only reason of spiking. To predict the level of noise intensity needed to generate spikes, the confidence-domain method is used, which is based on the stochastic sensitivity function. The main characteristics of interspike intervals depending on the intensity of the noise are also described. The second chapter is devoted to the application of the method of the stochastic sensitivity function to attractors of a piecewise-smooth one-dimensional map, which describes the population dynamics. The first stage of the study is a parametric analysis of the possible regimes of the deterministic model: determining the zones of existence of stable equilibria and chaotic attractors. The theory of critical points is used to determine the parametric boundaries of a chaotic attractor. In the case where the system is affected by a random noise, based on the stochastic sensitivity function, a description of the spread of random states around equilibrium and a chaotic attractor is given. A comparative analysis of the influence of parametric and additive noise on the attractors is carried out. Using the technique of confidence intervals, the probabilistic mechanisms of extinction of a population under the influence of noise are studied. Changes in the parametric boundaries of the existence of population under the influence of random disturbance are analyzed. In the third chapter the possible dynamic modes of the Lotka-Volterra model in determi\-nistic and stochastic cases are analyzed. Depending on the two parameters of the system, bifurcation diagram is constructed. Parametric zones of the existence of stable equilibria, cycles, closed invariant curves, and also chaotic attractors are studied. The bifurcations of the period doubling, Neimark--Sacker and the crisis are described. The complex shape of the basins of attraction is demonstrated. In addition to the deterministic system, the stochastic system is studied in detail, which describes the influence of external random disturbance. In the case of chaos, an algorithm for finding critical lines describing the boundary of a chaotic attractor is given. Based on the stochastic sensitivity function, confidence bands and ellipses are constructed to describe the spread of random states around a deterministic attractor.
22
Andrade, Vinícius Santos. "Análise da dinâmica caótica de pêndulos com excitação paramétrica no suporte." Universidade de São Paulo, 2003. http://www.teses.usp.br/teses/disponiveis/18/18133/tde-26022016-144941/.
Abstract:
Este trabalho apresenta a modelagem de um problema representado por um pêndulo elástico com excitação paramétrica vertical do suporte e a análise de estabilidade do sistema pendular que se obtém desconsiderando a elasticidade do pêndulo. A modelagem dos pêndulos e a obtenção das equações do movimento são feitas a partir da equação de Lagrange, utilizando as leis de Newton e para a análise de estabilidade do sistema pendular são apresentados os diagramas de bifurcações, multiplicadores de Floquet, mapas e seções de Poincaré e expoentes de Lyapunov. O comportamento do sistema pendular com excitação paramétrica vertical do suporte é investigado através de simulação computacional e apresentam-se resultados para diferentes faixas de valores da amplitude de excitação externa.This work presents the modeling of an elastic pendulum with parametric excitation of the support and the analysis of the stability of the pendulum that one obtains disregarding the elasticity of the pendulum. The modeling of the pendulum and the equation of motions are obtained from the Lagrange\'s equations, using Newton\'s law. The concepts of bifurcation, Floquet\'s multipliers, Poincaré maps and sections and Lyapunov exponent are presented for the analysis of stability. The behavior of the pendulum with parametric excitation of the suport is investigated through computational simulation and results for different intervals of values of the external excitation amplitude are presented.
23
Duarte, Jorge das Neves. "Comportamento caótico em sistemas fisiológicos." Doctoral thesis, Universidade de Évora, 2006. http://hdl.handle.net/10174/11109.
Abstract:
Neste trabalho estudamos a dinâmica de modelos biofísicos caóticos que representam a actividade eléctrica de células excitáveis.
Usando técnicas da teoria dos sistemas dinâmicos, quantificamos a complexidade das estruturas fisiológicas através da análise de determinadas aplicações no intervalo. Mais precisamente, caracterizamos a entropia topológica e um segundo invariante topológico, denotado por r, com o propósito de descrever o comportamento caótico dos modelos.
Primeiramente, apresentamos um estudo da dinâmica de um modelo do tipo FitzHugh-Nagumo submetido a um estímulo periódico.
No contexto dos ritmos fisiológicos, proporcionamos uma caracterização da dinâmica de uma família de aplicações na circunferência que foi proposta como modelo para osciladores não lineares periodicamente forçados.
Atendendo à sua importância, analisamos modelos biofísicos para o comportamento "explosivo" de células excitáveis. A dinâmica de uma célula singular e a caracterização do efeito de acoplamento em células "explosivas" idênticas, é particularmente interessante para o nosso estudo.
Finalmente, apresentamos algumas considerações sobre a relevância do comportamento caótico em sistemas neuronais como factor crucial de adaptação a um meio em constante evolução./ABSTRACT - In this work we study the dynamics of chaotic biophysical models that
represent the electrical activity of excitable cells.
Using techniques of dynamical systems theory, we quantify the complexity of the physiological
structures, through the analysis of specific maps on the interval. More precisely,
we characterize the topological entropy and a second topological invariant, denoted by r,
in order to describe the chaotic behavior of the models.
Firstly, we present a study of the dynamics of a FitzHugh-Nagumo type model under
periodic function forcing.
In the context of physiological rhythms, we provide a characterization of the dynamics of
a family of circle maps that has been proposed as a model for periodically forced
nonlinear oscillators.
Regarding their importance, we analyse biophysical models for the bursting behavior
of excitable cells. The dynamics of a single cell and the characterization of the effect of
coupling on identical bursting cells, is particularly interesting for our study.
Finally, we present some considerations about the relevance of the chaotic behavior in
neural systems as a crucial factor of adaptation to an environment in constant evolution.
24
Nazé, Pierre Marie Antoine Leite. "Tempos de primeira-passagem como medida de informação em sistemas fracamente caóticos." reponame:Repositório Institucional da UFABC, 2015.
Abstract:
Orientador: Prof. Dr. Roberto VenegerolesDissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2015.
Discutiremos uma classe de sistemas dinâmicos intermitentes na qual o espaço de fase é composto de duas regiões distintas: uma região laminar, onde a partícula desenvolve uma dinâmica lenta e quase regular até saltar para uma região turbulenta, onde a mesma desenvolve uma dinâmica caó- tica de curta duração até ser reinjetada de volta para a fase laminar, num processo que assim se repete. A fase laminar é causada pela existência de medida invariante innita, e a composição regularidade-caos resulta numa modalidade de caos fraco na qual a separação de trajetórias inicialmente muito próximas torna-se subexponencial (em sistemas caóticos usuais, essa separação é exponencial). Por conta desse tipo intermitência, o mapa apresentará um comportamento ergódico diferente daquele observado pelo teorema de Birkho, de modo que a distribuição de médias temporais de observáveis (com fatores próprios de normalização) é descrita essencialmente por uma estatística Mittag-Leer, ao invés de distribuições com limites assintóticos para delta de Dirac. Apresentaremos a lei responsável por tal comportamento, o teorema de Aaronson-Darling-Kac, que nos permitirá estender adequadamente certos observáveis, tais como o expoente de Lyapunov e a entropia de Kolmogorov- Sinai, de modo a inferir precisamente a existência desse tipo de instabilidade. Após um estudo das principais características ergódicas de tais sistemas, investigamos o número de primeiras-passagens da fase laminar para a turbulenta, e como obter informações-chave por meio dessa quantidade. Mostraremos também que a teoria de processos de renovação, usualmente empregada na literatura para esse m, é insuciente para descrever precisamente esse tipo de intermitência. Historicamente, esse tipo de sistema surgiu do estudo de mapas de primeiro retorno de certas seções do atrator de Lorenz, realizado nos anos 80 por Pomeau e Manneville. Atualmente, cadeias de tais mapas são empregadas no estudo de difusão anômala e passeios aleatórios com tempos de espera.
We discuss a class of intermittent dynamical systems in which the phase space is made up of two distinct regions: a laminar region, where the particle develops a slow and almost regular dynamic until it jumps to a turbulent region, where it develops a chaotic dynamic of short duration that is reinjected back into the laminating step, in a repeating process. The laminar phase is caused by the existence of innite invariant measure, and the regularity-chaos composition results in a weak mode in which the trajectories separation of two initial nearly points becomes subexponential (in usual chaotic systems, this separation is exponential). Because of this type of intermittency, the map will present a dierent behavior from that observed by ergodic Birkho's theorem, so that the distribution of average observable time (with its own normalization factors) is described essentially by a Mittag-Leer statistics, rather than distributions with asymptotic limit to the Dirac delta. We will present the law responsible for such behavior, the theorem Aaronson-Darling-Kac, which will allow us to extend properly certain observables, such as the Lyapunov exponent and entropy Kolmogorov-Sinai, in order to infer precisely the existence of such instability . After a study of the main ergodic characteristics of such systems, we investigate the number of rst-passages of the laminar stage for the turbulence, and how to get key information by that amount. We will also show that the theory of renewal processes, usually used in the literature for this purpose, is insucient to accurately describe this type of intermittency. Historically, this type of system emerged from the study of rst return maps of certain sections of the Lorenz attractor was accomplished in the 80's by Pomeau and Manneville. Currently chains of these maps are used in the study of anomalous diusion and random walks with waiting times.
25
Puma, Samuelsson Calixto. "Utsidan ger insidan en chans - En blandad metodstudie om vad vita svenskar tycker är viktigast av gemensam ras eller gemensam etnicitet i valet av vem man vill dejta." Thesis, Malmö universitet, Fakulteten för kultur och samhälle (KS), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:mau:diva-21144.
Abstract:
The purpose of this study is to investigate what is most important of common race or common ethnicity in the choice of who you want to date. This study highlights how white swedes select and reason about whom one wants to date based on common race and common ethnicity. Gordon Allport's theory of Social categorisation was chosen as a theoretical starting point, based on the purpose of this study. The analysis is based on 20 quantitative surveys and 6 qualitative interviews. The overall data that was collected focused on who you want to date in terms of common race and common ethnicity, but the surveys leaned towards the selection between common race or common ethnicity and the interviews leaned towards the reasoning behind the selection between race and ethnicity. The result shows that the majority of the respondents could consider to date anyone regardless of common race or common ethnicity. But having to choose between common race and common ethnicity, common ethnicity was more important.
26
Bartoloni, Bruno Figueiredo. "Mapas simpléticos com correntes reversas em tokamaks." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/43/43134/tde-22112016-211638/.
Abstract:
Desenvolvemos um modelo na forma de um mapeamento bidimensional simplético (conservativo) para estudar a evolução das linhas de campo magnético de um plasma confinado no interior de um tokamak. Na primeira parte, consideramos dois perfis estudados na literatura para a densidade de corrente no plasma: um monotônico e um não-monotônico, que dão origem a diferentes perfis analíticos do fator de segurança. Nas simulações, consideramos inicialmente o sistema no equilíbrio, onde observamos, nas seções de Poincaré, apenas linhas invariantes. Em seguida, adicionamos uma perturbação (corrente externa), onde observamos cadeias de ilhas e caos no sistema. Na segunda parte consideramos um perfil também não-monotônico, mas com uma região na qual a densidade de corrente no plasma torna-se negativa, estudo ainda em aberto na literatura, que causa uma divergência no perfil do fator de segurança. Mesmo considerando o sistema apenas no equilíbrio, surgiram cadeias de ilhas muito pequenas em torno de curvas sem shear e caos localizado no sistema, característica não verificada para os outros perfis estudados no equilíbrio. Variando parâmetros relacionados à expressão da densidade de corrente, conseguimos controlar o aparecimento de regiões com cadeias de ilhas em torno de curvas sem shear e regiões caóticas. Para comprovar os resultados, aplicamos o perfil considerado a um outro mapa simplético da literatura (tokamap). Na parte final, consideramos a configuração do perfil do fator de segurança na forma de um divertor. Nessa configuração também temos uma divergência na expressão do perfil do fator de segurança. Observamos características similares (cadeias de ilhas em torno de curvas sem shear e caos) quando consideramos o perfil não-monotônico com densidade de corrente reversa.We develop a symplectic (conservative) bidimensional map to study the evolution of magnetic field lines of a confined plasma in a tokamak. First, we considered two profiles for the plasma current density, studied in the literature: monotonic and non-monotonic, which give rise to different profiles for the poloidal magnetic field and different analytical profiles for the safety factor. In our simulations, we consider the system initially at equilibrium, where we observe, in Poincaré sections, only invariant lines. Then, we add a perturbation (external current), where we observe island chains and chaos in the system. In the second part, we consider a non-monotonic profile, but with a region which the current density becomes negative, which causes a divergence in the safety factor profile. Even considering only the sistem at equilibrium, very small island chains appeared around the shearless curves, and localized chaos. This feature was not observed for the other profiles at equilibrium. We can control the appearance of the regions with island chaind around the shearless curves and chaotic regions, by variation of parameters related to the density current expression. To comprove our results, we aplly the same profile to the other symplectic map. Finally, we consider a safety factor profile in a divertor configuration. We also have a divergence on in the safety factor profile. We observe similar features (island chains around shearless curves and localized chaos) when we consider a non-monotonic safety factor profile with a reversed density current.
27
Zhang, Qiong. "Ambivalence & ambiguity Chinese-American literature beyond politics and ethnography = Mao dun qing jie yu yi shu mo hu xing : chao yue zheng zhi he zu yi de Meiguo Hua yi wen xue /." Shanghai : Fu dan da xue chu ban she, 2006. http://books.google.com/books?id=cQ1IAAAAMAAJ.
28
Kositsakulchai͏̈, Ekasit. "Modélisation de la dynamique de l'hydrosystème du bassin du Mae Klong (Thai͏̈lande). Une esquisse de système interactif d'aide à la décision pour la gestion de l'eau." Montpellier 2, 2001. http://www.theses.fr/2001MON20008.
Abstract:
La modelisation de la gestion integree de la ressource en eau dans le bassin versant du mae klong (31 000 km 2) s'appuie sur l'approche systemique. La variabilite de la ressource et l'intensification des usages (production hydroelectrique, irrigation, alimentation en eau potable, protection contre les intrusions salines, tourisme ecologique) incitent a une gestion prudente des hydrosystemes amenages. Pour aborder des conditions dynamiques complexes, les modeles de simulation qui prennent en compte des regles de gestion parfaitement definies jouent un role crucial. L'analyse systemique, d'une part, et l'outil de modelisation vensim, base sur les methodes de dynamique des systemes, d'autre part, constituent des moyens d'analyse et de representation des systemes complexes. Deux types de modeles sont mis en uvre : un modele pluie-debit pour estimer les ressources en eau en plusieurs points de controle du bassin versant et un modele de decision integrant la conduite operationnelle des ouvrages, les contraintes reglementaires et l'evaluation economique.
29
Nilsson, Erik. "Waves of change : traditional religion among the Urak Lawoi, sea nomads of Ko Lanta, Thailand." Thesis, University of Gävle, Ämnesavdelningen för kultur- och religionsvetenskap, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-6359.
Abstract:
This essay is the result of a field study in Ko Lanta in Thailand, during October-December 2009. The purpose of the study was to document the traditional religion of Urak Lawoi and to analyze in what way their life and beliefs have changed during the last 20 years.
Urak Lawoi is the name of one of the sea nomadic ethnic groups who lives along the shores of Myanmar, Thailand and Malaysia. They are spread on many of the islands in the Andaman Sea archipelago and Ko Lanta is the main settlement. Ural Lawoi is regarded as the indigenous people of the island and they live there as a minority with Muslims and Thai-Chinese.
The traditional religion of Urak Lawoi is built upon the animistic belief of their ancestors. The religious leader and link between the spirit world and the humans is the To Maw. The family bonds are strong in the Urak Lawoi community and the elders play an important role in life and after death, when they can keep on watching out for their offspring. For the living it is important to do the rituals and ceremonies in the right way to obtain good luck and avoid bad luck.
In the last 20 years Ko Lanta has experienced a tremendous process of change caused by the increasing tourism. The conditions of the Urak Lawoi and their way of life have dramatically changed. The modern society with money economy, new technical solutions and a rationalized large-scale fishing has rapidly changed their way of life. The tsunami catastrophe, and the following attention from help organizations and missionary activities, has escalated the process. The traditional religion and culture of the Urak Lawoi is still present on the island but it is declining and changing under the influence of the constant pressure from other interests.
30
Nilsson, Erik. "Forces of change : A theoretical analysis of syncretism between Theravada Buddhism and animistic indigenous beliefs in Thailand." Thesis, Högskolan i Gävle, Avdelningen för kultur-, religions- och utbildningsvetenskap, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:hig:diva-8073.
Abstract:
Urak Lawoi is the name of one of the sea nomadic tribes which lives along the shores of Myanmar, Thailand and Malaysia. They are spread on many of the islands in the Andaman Sea archipelago and Ko Lanta is the main settlement. Urak Lawoi is regarded as the indigenous people of the island and they live there as a minority together with Muslims and Thai-Chinese. The traditional religion and culture of Urak Lawoi is built upon the animistic belief of their ancestors. In the last 20 years Ko Lanta has experienced a tremendous process of change caused by increasing tourism. The conditions of the Urak Lawoi and their way of life have dramatically changed. The fact that this process brings consequences for the traditional culture and religion is obvious, but in what direction is it developing? To be able to interpret and expound the material from my field studies among Urak Lawoi on Ko Lanta in October-December 2009, I have done a literature search to investigate the animistic traditions and the syncretistic nature of belief in Thailand. I have also tried to find theories about the process of religious change and the forces working behind them. In this essay I am trying to do a theoretical analysis of the field study material using theories and parallel examples I have found in the literature.
31
Priyadarshini, Itishree. "Spatiotemporal Chaos in Coupled Map Lattice." Thesis, 2011. http://ethesis.nitrkl.ac.in/2694/2/report.pdf.
Abstract:
"sensitive dependence on initial condition", which is the essential feature of chaos is demonstrated through simple Lorenz model. Period doubling route to chaos is shown by analysis of Logistic map and other different route to chaos is discussed. Coupled map lattices are investigated as a model for spatio-temporal chaos. Diffusively coupled logistic lattice is studied which shows different pattern in accordance with the coupling constant and the non-linear parameter i.e. frozen random pattern, pattern selection with suppression of chaos , Brownian motion of the space defect, intermittent collapse, soliton turbulence and travelling waves.
32
Chung, Wen-Chin, and 鍾文欽. "Behavior of Coupled Logistic Map and Controlling Chaos." Thesis, 2001. http://ndltd.ncl.edu.tw/handle/46893541720540769007.
33
LaMacchia, Brian, and Jason Nieh. "The Standard Map Machine." 1989. http://hdl.handle.net/1721.1/6015.
Abstract:
We have designed the Standard Map Machine(SMM) as an answer to the intensive computational requirements involved in the study of chaotic behavior in nonlinear systems. The high-speed and high-precision performance of this computer is due to its simple architecture specialized to the numerical computations required of nonlinear systems. In this report, we discuss the design and implementation of this special-purpose machine.
34
Nieh, Jason. "Using Special-Purpose Computing to Examine Chaotic Behavior in Nonlinear Mappings." 1989. http://hdl.handle.net/1721.1/6822.
Abstract:
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.
35
Meyerson, Dmitry. "Electostatic plasma edge turbulence and anomalous transport in SOL plasmas." Thesis, 2014. http://hdl.handle.net/2152/27160.
Abstract:
Controlling the scrape-off layer (SOL) properties in order to limit divertor erosion and extend component lifetime will be crucial to successful operation of ITER and devices that follow, where intermittent thermal loads on the order of GW/m² are expected. Steady state transport in the edge region is generally turbulent with large, order unity, fluctuations and is convection dominated. Owing to the success of the past fifty years of progress in magnetically confining hot plasmas, in this work we examine convective transport phenomena in the SOL that occur in the relatively "slow", drift-ordered fluid limit, most applicable to plasmas near MHD equilibrium. Diamagnetic charge separation in an inhomogeneous magnetic field is the principal energy transfer mechanism powering turbulence and convective transport examined in this work. Two possibilities are explored for controlling SOL conditions. In chapter 2 we review basic physics underlying the equations used to model interchange turbulence in the SOL and use a subset of equations that includes electron temperature and externally applied potential bias to examine the possibility of suppressing interchange driven turbulence in the Texas Helimak. Simulated scans in E₀×B₀ flow shear, driven by changes in the potential bias on the endplates appears to alter turbulence levels as measured by the mean amplitude of fluctuations. In broad agreement with experiment negative biasing generally decreases the fluctuation amplitude. Interaction between flow shear and interchange instability appears to be important, with the interchange rate forming a natural pivot point for observed shear rates. In chapter 3 we examine the possibility of resonant magnetic perturbations (RMPs) or more generally magnetic field-line chaos to decrease the maximum particle flux incident on the divertor. Naturally occurring error fields as well as RMPs applied for stability control are known to cause magnetic field-line chaos in the SOL region of tokamaks. In chapter 3 2D simulations are used to investigate the effect of the field-line chaos on the SOL and in particular on its width and peak particle flux. The chaos enters the SOL dynamics through the connection length, which is evaluated using a Poincaré map. The variation of experimentally relevant quantities, such as the SOL gradient length scale and the intermittency of the particle flux in the SOL, is described as a function of the strength of the magnetic perturbation. It is found that the effect of the chaos is to broaden the profile of the sheath-loss coefficient, which is proportional to the inverse connection length. That is, the SOL transport in a chaotic field is equivalent to that in a model where the sheathloss coefficient is replaced by its average over the unperturbed flux surfaces. Both fully chaotic and the flux-surface averaged approximation of RMP application significantly lower maximum parallel particle flux incident on the divertor.text
36
Müller-Bender, David. "Nonlinear Dynamics and Chaos in Systems with Time-Varying Delay." 2020. https://monarch.qucosa.de/id/qucosa%3A72483.
Abstract:
Systeme mit Zeitverzögerung sind dadurch charakterisiert, dass deren zukünftige Entwicklung durch den Zustand zum aktuellen Zeitpunkt nicht eindeutig festgelegt ist. Die Historie des Zustands muss in einem Zeitraum bekannt sein, dessen Länge Totzeit genannt wird und die Gedächtnislänge festlegt. In dieser Arbeit werden fundamentale Effekte untersucht, die sich ergeben, wenn die Totzeit zeitlich variiert wird.
Im ersten Teil werden zwei Klassen periodischer Totzeitvariationen eingeführt. Da diese von den dynamischen Eigenschaften einer eindimensionalen iterierten Abbildung abgeleitet werden, die über die Totzeit definiert wird, werden die Klassen entsprechend der zugehörigen Dynamik konservativ oder dissipativ genannt. Systeme mit konservativer Totzeit können in Systeme mit konstanter Totzeit transformiert werden und besitzen gleiche charakteristische Eigenschaften. Dagegen weisen Systeme mit dissipativer Totzeit fundamentale Unterschiede z.B. in der Tangentialraumdynamik auf. Im zweiten Teil werden diese Ergebnisse auf Systeme angewendet, deren Totzeit im Vergleich zur internen Relaxationszeit des Systems groß ist. Es zeigt sich, dass ein durch dissipative Totzeitvariationen induzierter Mechanismus, genannt resonanter Dopplereffekt, unter anderem zu neuen Arten chaotischer Dynamik führt. Diese sind im Vergleich zur bekannten chaotischen Dynamik in Systemen mit konstanter Totzeit sehr niedrig-dimensional. Als Spezialfall wird das so genannte laminare Chaos betrachtet, dessen Zeitreihen durch nahezu konstante Phasen periodischer Dauer gekennzeichnet sind, deren Amplitude chaotisch variiert. Im dritten Teil dieser Arbeit wird auf der Basis experimenteller Daten und durch die Analyse einer nichtlinearen retardierten Langevin-Gleichung gezeigt, dass laminares Chaos robust gegenüber Störungen wie zum Beispiel Rauschen ist und experimentell realisiert werden kann. Es werden Methoden zur Zeitreihenanalyse entwickelt, um laminares Chaos in experimentellen Daten ohne Kenntnis des erzeugenden Systems zu detektieren. Mit diesen Methoden ist selbst dann eine Detektion möglich, wenn das Rauschen so stark ist, dass laminares Chaos mit bloßem Auge nur schwer erkennbar ist.:1. Introduction
2. Dissipative and conservative delays in systems with time-varying delay
3. Laminar Chaos and the resonant Doppler effect
4. Laminar Chaos: a robust phenomenon
5. Summary and concluding remarks
A. AppendixIn systems with time-delay, the evolution of a system is not uniquely determined by the state at the current time. The history of the state must be known for a time period of finite duration, where the duration is called delay and determines the memory length of the system. In this work, fundamental effects arising from a temporal variation of the time-delay are investigated. In the first part, two classes of periodically time-varying delays are introduced. They are related to a specific dynamics of a one-dimensional iterated map that is defined by the time-varying delay. Referring to the related map dynamics the classes are called conservative or dissipative. Systems with conservative delay can be transformed into systems with constant delay, and thus have the same characteristic properties as constant delay systems. In contrast, there are fundamental differences, for instance, in the tangent space dynamics, between systems with dissipative delay and systems with constant delay. In the second part, these results are applied to systems with a delay that is considered large compared to the internal relaxation time of the system. It is shown that a mechanism induced by dissipative delays leads to new kinds of regular and chaotic dynamics. The dynamics caused by the so-called resonant Doppler effect is fundamentally different from the behavior known from systems with constant delay. For instance, the chaotic attractors in systems with dissipative delay are very low-dimensional compared to typical ones arising in systems with constant delay. An example of this new kind of low-dimensional dynamics is given by the so-called Laminar Chaos. It is characterized by nearly constant laminar phases of periodic duration, where the amplitude varies chaotically. In the third part of this work, it is shown that Laminar Chaos is a robust phenomenon, which survives perturbations such as noise and can be observed experimentally. Therefore experimental data is provided and a nonlinear delayed Langevin equation is analyzed. Using the robust features that characterize Laminar Chaos, methods for time series analysis are developed, which enable us to detect Laminar Chaos without the knowledge of the specific system that has generated the time series. By these methods Laminar Chaos can be detected even for comparably large noise strengths, where the characteristic properties are nearly invisible to the eye.:1. Introduction 2. Dissipative and conservative delays in systems with time-varying delay 3. Laminar Chaos and the resonant Doppler effect 4. Laminar Chaos: a robust phenomenon 5. Summary and concluding remarks A. Appendix
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(10702248), Hugo Esquivel. "Efficient Spectral-Chaos Methods for Uncertainty Quantification in Long-Time Response of Stochastic Dynamical Systems." Thesis, 2021.
Abstract:
Uncertainty quantification techniques based on the spectral approach have been studied extensively in the literature to characterize and quantify, at low computational cost, the impact that uncertainties may have on large-scale engineering problems. One such technique is the generalized polynomial chaos (gPC) which utilizes a time-independent orthogonal basis to expand a stochastic process in the space of random functions. The method uses a specific Askey-chaos system that is concordant with the measure defined in the probability space in order to ensure exponential convergence to the solution. For nearly two decades, this technique has been used widely by several researchers in the area of uncertainty quantification to solve stochastic problems using the spectral approach. However, a major drawback of the gPC method is that it cannot be used in the resolution of problems that feature strong nonlinear dependencies over the probability space as time progresses. Such downside arises due to the time-independent nature of the random basis, which has the undesirable property to lose unavoidably its optimality as soon as the probability distribution of the system's state starts to evolve dynamically in time.
Another technique is the time-dependent generalized polynomial chaos (TD-gPC) which utilizes a time-dependent orthogonal basis to better represent the stochastic part of the solution space (aka random function space or RFS) in time. The development of this technique was motivated by the fact that the probability distribution of the solution changes with time, which in turn requires that the random basis is frequently updated during the simulation to ensure that the mean-square error is kept orthogonal to the discretized RFS. Though this technique works well for problems that feature strong nonlinear dependencies over the probability space, the TD-gPC method possesses a serious issue: it suffers from the curse of dimensionality at the RFS level. This is because in all gPC-based methods the RFS is constructed using a tensor product of vector spaces with each of these representing a single RFS over one of the dimensions of the probability space. As a result, the higher the dimensionality of the probability space, the more vector spaces needed in the construction of a suitable RFS. To reduce the dimensionality of the RFS (and thus, its associated computational cost), gPC-based methods require the use of versatile sparse tensor products within their numerical schemes to alleviate to some extent the curse of dimensionality at the RFS level. Therefore, this curse of dimensionality in the TD-gPC method alludes to the need of developing a more compelling spectral method that can quantify uncertainties in long-time response of dynamical systems at much lower computational cost.
In this work, a novel numerical method based on the spectral approach is proposed to resolve the curse-of-dimensionality issue mentioned above. The method has been called the flow-driven spectral chaos (FSC) because it uses a novel concept called enriched stochastic flow maps to track the evolution of a finite-dimensional RFS efficiently in time. The enriched stochastic flow map does not only push the system's state forward in time (as would a traditional stochastic flow map) but also its first few time derivatives. The push is performed this way to allow the random basis to be constructed using the system's enriched state as a germ during the simulation and so as to guarantee exponential convergence to the solution. It is worth noting that this exponential convergence is achieved in the FSC method by using only a few number of random basis vectors, even when the dimensionality of the probability space is considerably high. This is for two reasons: (1) the cardinality of the random basis does not depend upon the dimensionality of the probability space, and (2) the cardinality is bounded from above by M+n+1, where M is the order of the stochastic flow map and n is the order of the governing stochastic ODE. The boundedness of the random basis from above is what makes the FSC method be curse-of-dimensionality free at the RFS level. For instance, for a dynamical system that is governed by a second-order stochastic ODE (n=2) and driven by a stochastic flow map of fourth-order (M=4), the maximum number of random basis vectors to consider within the FSC scheme is just 7, independent whether the dimensionality of the probability space is as low as 1 or as high as 10,000.
With the aim of reducing the complexity of the presentation, this dissertation includes three levels of abstraction for the FSC method, namely: a specialized version of the FSC method for dealing with structural dynamical systems subjected to uncertainties (Chapter 2), a generalized version of the FSC method for dealing with dynamical systems governed by (nonlinear) stochastic ODEs of arbitrary order (Chapter 3), and a multi-element version of the FSC method for dealing with dynamical systems that exhibit discontinuities over the probability space (Chapter 4). This dissertation also includes an implementation of the FSC method to address the dynamics of large-scale stochastic structural systems more effectively (Chapter 5). The implementation is done via a modal decomposition of the spatial function space as a means to reduce the number of degrees of freedom in the system substantially, and thus, save computational runtime.
38
Weirauch, Angelika. "Kreativität – wie man Sinn und Freude im Chaos der Existenz findet." Master's thesis, 2009. https://slub.qucosa.de/id/qucosa%3A3296.
Abstract:
Die Arbeit befasst sich mit unterschiedlichen philosophischen, psychologischen und erziehungswissenschaftlichen Ansätzen der Kreativitätsforschung und mit einem Selbstversuch. Eine These ist, dass veränderte Bewusstseinszustände (wie z.B. Schlaf, Rausch, Krankheit aber auch körperliche Ausarbeitung wie das Wandern) besondere Zugänge zur Kreativität sind.:1 Einleitung 2
1.1 Erkenntnisgewinn 2
1.2 Das Feld eingrenzen 2
1.3 Von den Ausgangspunkten in den Erkenntnisprozess 3
1.4 Methoden und Umgang mit den Quellen 4
2 Forschungen zur Kreativität 5
2.1 Persönlichkeit, Produkt und Prozess 6
2.1.1 Persönlichkeit 6
2.1.2 Produkt 9
2.1.3 Prozess 10
2.2 Lebenswege kreativer Menschen 10
2.2.1 Kindheit 11
2.2.2 Adoleszenz 11
2.2.3 Erwachsenenalter 12
2.2.4 Als Erwachsene/r geeignete Arbeitsbereiche finden 13
2.2.5 Selbstbild und Fremdbild als KünstlerIn oder ForscherIn 15
2.2.6 Persönlichkeitsmerkmale 15
2.3. Künstliche Kreativität (Wolfgang Bibel) 16
2.4 Dimensionen der Komplexität 20
2.5 Domäne, Feld und Persönlichkeit 22
2.5.1 Felder und Domänenwächter 23
2.5.2 System versus Individuum? 25
2.5.3 Kritik gegenüber der Feldeinteilung 26
2.6 Kreativität als Konstrukt (Hans Westmeyer) 28
3 Kreativitätsfördernde Voraussetzungen 31
3.1 Motivationen zur Kreativität – die Theorien psychologischer Schulen 34
3.2 Konvergierendes und divergierendes Denken 35
3.3 Die kulturellen Voraussetzungen 37
3.4 Die psychischen Voraussetzungen 42
3.5 Die Belohnungen 45
3.6 Die geschlechtsabhängigen Voraussetzungen 47
3.6.1 Zuschreibungen 47
3.6.2 Selbstaussagen 50
3.6.3 Sachargumente 51
3.6.4 Bedingungen der Ausübung von Kreativität 52
3.7 Wahrnehmung und Achtsamkeit (Karl-Heinz Brodbeck) 53
3.8 Veränderte Bewusstseinszustände 60
3.8.1 Rausch und Flow 60
3.8.2 Schlaf, Traum und Luzidtraum 65
3.8.3 Psychische Störungen 68
3.8.4 Wandern und Trance 74
4 Nichtalltägliche Zugänge zur Kreativität 77
4.1 Die Nachtseite der Wissenschaft (Ernst-Peter Fischer) 77
4.1.1 Die Einseitigkeit vieler Forschungen 78
4.1.2 Fehlende Ganzheitlichkeit 80
4.1.3 Archetypen 81
4.1.4 Symbole –Brücken zur Kreativität 82
4.1.5 Faszination und Glück 83
4.1.6 Sinn-Korrespondenz 85
4.2 Götterbeziehungen 86
4.2.1 Die Musen 86
4.2.2 Pegasus 87
4.2.3 Griechische und römische Mythologie 88
4.2.4 Christliche Mythologie 92
4.2.5 Asiatische Mythologie 95
4.2.6 Das Destruktive in den Religionen 97
4.3 Unbewusstes 98
4.4 Lebenskunst 102
4.5 Paradoxa 106
5 Die Bedeutung des Gehens für die Entfaltung der Kreativität 109
5.1 Die Weg-Metapher 112
5.2 Wallfahrten, Pilgern und die Peripatetiker 114
5.3 Selbstversuch Wandern 117
39
(8770355), Maaninee Gupta. "Finding Order in Chaos: Resonant Orbits and Poincaré Sections." Thesis, 2020.
Abstract:
Resonant orbits in a multi-body environment have been investigated in the past to aid the understanding of perceived chaotic behavior in the solar system. The invariant manifolds associated with resonant orbits have also been recently incorporated into the design of trajectories requiring reduced maneuver costs. Poincaré sections are now also extensively utilized in the search for novel, maneuver-free trajectories in various systems. This investigation employs dynamical systems techniques in the computation and characterization of resonant orbits in the higher-fidelity Circular Restricted Three-Body model. Differential corrections and numerical methods are widely leveraged in this analysis in the determination of orbits corresponding to different resonance ratios. The versatility of resonant orbits in the design of low cost trajectories to support exploration for several planet-moon systems is demonstrated. The efficacy of the resonant orbits is illustrated via transfer trajectory design in the Earth-Moon, Saturn-Titan, and the Mars-Deimos systems. Lastly, Poincaré sections associated with different resonance ratios are incorporated into the search for natural, maneuver-free trajectories in the Saturn-Titan system. To that end, homoclinic and heteroclinic trajectories are constructed. Additionally, chains of periodic orbits that mimic the geometries for two different resonant ratios are examined, i.e., periodic orbits that cycle between different resonances are determined. The tools and techniques demonstrated in this investigation are useful for the design of trajectories in several different systems within the CR3BP.
40
"Chaos et politique: limmense problème des guerres de religion en france au xvie siècle et ses acheminements." Tese, MAXWELL, 2003. http://www.maxwell.lambda.ele.puc-rio.br/cgi-bin/db2www/PRG_0991.D2W/SHOW?Cont=4366:pt&Mat=&Sys=&Nr=&Fun=&CdLinPrg=pt.