Les travaux effectués, dans le cadre de cette thèse, concernent l’analyse et la synthèse de systèmes dynamiques continus complexes de grande dimension. Pour la classe des systèmes étudiés, est mise en exergue en particulier l’importance du choix de la description des systèmes sur l’étendue des résultats pouvant être obtenus lorsque la méthode d’étude de la stabilité est fixée.L’utilisation des normes vectorielles comme fonction d’agrégation et du critère pratique de Borne et Gentina pour l’étude de la stabilité, associée à la description des systèmes par des matrices caractéristiques de forme en flèche, a permis l’élaboration de nouvelles conditions suffisantes de stabilisabilité de systèmes dynamiques continus non linéaires, monovariables et multivariables, formulées en théorèmes et corollaires.Ces résultats obtenus, pour une classe de processus, pouvant être caractérisés par des matrices instantanées de forme en flèche mince, ont été généralisés au cas des matrices quelconques, pouvant être mises sous forme en flèche mince généralisée ou en flèche épaisse.Les critères élaborés, soit pour l’analyse de la stabilité soit pour la synthèse d’une loi de commande stabilisante, sont ensuite exploités, avec succès, pour la formulation de nouvelles conditions suffisantes de vérification des propriétés de synchronisation, d’anti-synchronisation et de synchronisation hybride de systèmes chaotiques du type maître-esclave, d’un grand intérêt, en particulier, pour garantir une transmission sécurisée / This Thesis deals with the analysis and the synthesis of dynamic large scale continuous systems depending on the choice of the system description.Stability and stabilisability proposed studies are based on the use of vector norms as an aggregation function and of the practical Borne-Gentina criterion, associated to the description of the system by instantaneous characteristic matrix in arrow form.Practical stability conditions, easy to use, are obtained for both dynamic nonlinear continuous single input single output systems and multiple inputs multiple outputs ones, formulated by means of theorems and corollaries. These obtained results for thin arrow form, are generalized to the case of matrices, which can be putted under thin generalized arrow form or thick arrow form. The proposed stability and stabilisability criteria are afterwards, successfully, exploited to formulate new sufficient conditions, guaranteeing the synchronization, the anti-synchronization and the hybrid synchronization properties, for chaotic master-slave systems, having an increasing interest throughout their application in the secure communication field

Submitted by Helmut Patrocinio (hell.kenn@gmail.com) on 2017-12-01T23:43:39Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Heloisa_Onias_Dissertacao_2012.pdf: 9805428 bytes, checksum: 00e0f3bac6584320107351966c70da69 (MD5) / Approved for entry into archive by Ismael Pereira (ismael@neuro.ufrn.br) on 2017-12-04T12:33:01Z (GMT) No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Heloisa_Onias_Dissertacao_2012.pdf: 9805428 bytes, checksum: 00e0f3bac6584320107351966c70da69 (MD5) / Made available in DSpace on 2017-12-04T12:33:37Z (GMT). No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Heloisa_Onias_Dissertacao_2012.pdf: 9805428 bytes, checksum: 00e0f3bac6584320107351966c70da69 (MD5) Previous issue date: 2012-08 / O circuito RLD, formado por um resistor, um indutor e um diodo em s?rie, apresenta uma din?mica muito rica quando for?ado por uma tens?o externa harm?nica e vem sendo estudado h? d?cadas. Contudo, ainda existem t?picos em din?mica n?o-linear sendo estudados com variantes deste circuito. Varreduras nos par?metros de controle podem fazer com que esse sistema oscile eletronicamente entre regi?es peri?dicas e regi?es ca?ticas. O diodo ? o elemento n?o linear respons?vel pelo surgimento do caos. Utilizando um modelo de capacit?ncia n?o linear para descrever o comportamento do diodo, podemos escrever as equa??es para esse sistema e estudar a sua din?mica numericamente. Nosso principal objetivo foi o estudo de expoentes cr?ticos complexos em bifurca??es din?micas. Para isso, realizamos um estudo num?rico do circuito RLD for?ado senoidalmente utilizando como par?metros de controle a frequ?ncia e a amplitude da tens?o de entrada. Constru?mos, a partir das s?ries temporais da corrente total e da tens?o no diodo, diagramas de bifurca??o com diferentes cortes estrobosc?picos, que apresentam cascata de dobramento de per?odo, janelas peri?dicas e transi??o intermitente. Tamb?m realizamos estudos num?ricos do comportamento da m?dia na regi?o de transi??o caos-peri?dico na busca de encontrar um expoente cr?tico caracter?stico e oscilas??es na m?dia, elementos que j? foram observados no mapa log?stico. N?o foram poss?veis observar numericamente as oscila??es, mas observamos um decaimento exponencial com expoente cr?tico de aproximadamente 0,5. Montamos um sistema de controle, aquisi??o e tratamento de dados experimentais no qual ? poss?vel a realiza??o remota de experimentos simult?neos com dois circuitos diferentes. Obtivemos diagramas de bifurca??es experimentais nos quais observamos que o sistema apresentahisterese e alta sensibilidade ?s condi??es do experimento como, por exemplo, o passo de varredura do par?metro de controle. / The RLD circuit, formed by a resistor, an inductor and a diode in series, displays a very rich dynamics when forced by an external harmonic voltage, and it has being studied for decades. However, there are some topics in nonlinear dynamics that are still studied with variants of this circuit nowadays. Changes in the control parameters may cause electronic oscillations between regular and chaotic regions.The diode is the nonlinear element responsible for the appearance of chaos. Using a nonlinear capacitance model to describe the behavior of the diode, we can write the equations for this system and study its dynamics numerically. Our main objective was the study of critical exponents in complex dynamic bifurcations. For that, we did a numerical study of the RLD circuit forced sinusoidally using as control parameters the amplitude of the input voltage and the frequency. We made, from the time series obtained, bifurcation diagrams with different stroboscopic cuts, which have cascade of period-doubling, periodic windows and intermittent transition. We also did numerical studies of the average behavior in the periodic-chaos transition region searching for characteristic critical exponent and oscilas??es on average, elements that have been observed in the logistic map. It was not possible to observe the oscillations numerically, but we observed an exponential decay with critical exponent of approximately 0.5. We set up a system able to control, acquire and process experimental data making it possible to perform remote simultaneous experiments with two different circuits. We have obtained experimental diagrams bifurcations in which we observe that the system has hysteresis and high sensitivity to the conditions of the experiment such as the step of scanning the control parameter.

Les vésicules sont utilisées d'une manière extensive comme modèle pour comprendre les dynamiques et les déformations des globules rouges au niveau individuel, mais aussi concernant les phénomènes collectives et la rhéologie. La membrane de la vésicule résiste à la flexion mais pas au cisaillement, contrairement aux globules rouges, néanmoins elles partagent plusieurs propriétés dynamiques avec les globules rouges, comme le tank-treading (mouvement en chenille de char) et le tumbling (mouvement de bascule) sous écoulement de cisaillement, ou les formes parachutes et slippers (pantoufles) sous un écoulement de Poiseuille. Les globules rouges sont connus pour former des trains de cellules (clusters) dans la microcirculation attribués à la nature attractive des interactions hydrodynamiques. Nous avons étudié numériquement plusieurs types de problème comme:(i) les dynamiques de cellules isolées, (ii) le couplage hydrodynamique entre globules rouges (en utilisant les vésicules comme modèle) soumis à un écoulement de Poiseuille sous différent confinements; (iii) l'agrégation des globules rouges et la formation de rouleaux; et (iv) le rôle des macromolécules dans la formation de clusters sous écoulement. les résultats obtenus apportent un nouveau regard à la physique des objets déformables et sont transposables au cas de l'écoulement des globules rouges dans la microcirculation. / Vesicles are extensively used as a model for understanding dynamicsand deformation of red blood cells at the individual level but also regarding collective phenomena and rheology. Vesicles' membranes withstand to bending butdo not have a shear resistance, unlike red blood cells, but they still share several dynamical properties with red blood cells, like tank-treading and tumbling under linear shear flow, or parachute and slipper shapes under Poiseuille flow. The red blood cells are known to form train of cells in the microcirculation attributed to attractive hydrodynamic interactions. We investigate numerically several kind of problems such as: (i) the dynamics of isolated cells; (ii) the hydrodynamic coupling between the red blood cells (by using vesicles as a model) subject to a Poiseuille flow under different confinements; (iii) the aggregation of red blood cells and formation of rouleaux; and (iv) the contribution of macromolecules in the formation of clusters under flow condition. The obtained results give a new insight into thephysics of deformable objects under confinement that are transposable to the flow of red blood cells in the microcirculation.

La présente thèse décrit un projet de recherche multidisciplinaire qui porte sur la reconnaissance de l’émotion dans les sons, couvrant les théories psychologiques, l’analyse du signal acoustique,l’apprentissage automatique et la dynamique chaotique.Dans nos interactions et nos relations sociales, nous dépendons considérablement de la communication de l’information et de notre perception des messages transmis. En fait, la communication se produit lorsque les signaux transmettent des informations entre une source et une destination. Le signal peut être verbal, et l’information est ensuite portée par des motifs sonores, tels que des mots. Dans la communication vocale non verbale, cependant,l’information peut être des modèles perceptifs qui véhiculent des indices affectifs, que nous percevons et évaluons sous la forme d’intentions, d’attitudes, d’humeurs et d’émotions.La prévalence de la composante affective peut être observée dans les interactions informatiques humaines (HCI) où le développement d’applications automatisées qui comprennent et expriment les émotions est devenu crucial. De tels systèmes doivent être significatifs et faciles à utiliser pour l’utilisateur final, de sorte que notre interaction avec eux devient une expérience positive. Bien que la reconnaissance automatique des émotions dans les sons ait reçu une attention accrue au cours des dernières années, il s’agit encore d’un jeune domaine de recherche.Non seulement cela contribue à l’informatique affective en général, mais il fournit également une compréhension approfondie de la signification des sons dans notre vie quotidienne.Dans cette thèse, le problème de la reconnaissance des affects est abordé à partir d’une double perspective: nous commençons par adopter une approche standard de l’analyse acoustique du signal, où nous examinons et expérimentons les fonctionnalités existantes pour déterminer leur rôle dans la communication émotionnelle. Ensuite, nous nous tournons vers la dynamique chaotique et la symbolisation des séries temporelles, pour comprendre le rôle de la dynamique inhérente des sons dans l’expressivité affective. Nous menons nos études dans le contexte des sons non verbaux, à savoir les sons vocaux, musicaux et environnementaux.D’un point de vue de l’écoute humaine, une tâche d’annotation est menée pour construire un ground-truth de voix de chant non verbales, marquées par des descriptions catégoriques du modèle bidimensionnel d’émotions. Deux types de sons sont inclus dans l’étude: vocal et glottal.D’un point de vue psychologique, la présente recherche porte sur un débat qui existe depuis longtemps parmi les scientifiques et les psychologues, concernant les origines communes de la musique et de la voix. La question est abordée à partir d’une analyse acoustique ainsi que d’une approche dynamique non linéaire.D’un point de vue de la modélisation, ce travail propose une nouvelle approche dynamique non linéaire pour la reconnaissance de l’affect dans le son, basée sur la dynamique chaotique et la symbolisation adaptative des séries temporelles. Tout au long de cette thèse, les contrastes clés dans l’expressivité de l’émotion sont illustrés parmi les différents types de sons, à travers l’analyse des propriétés acoustiques, les métriques de la dynamique non linéaire et les performances des prédictions.Enfin, d’un point de vue progressif, nous suggérons que les travaux futurs étudient des caractéristiques motivées par les études cognitives. Nous suggérons également d’examiner dans quelle mesure nos caractéristiques reflètent les processus cognitifs. En outre, nous recommandons que nos fonctionnalités dynamiques soient testées dans des études à grande échelle de la reconnaissance d’émotions à travers la participation aux défis expérimentaux, dans le but de vérifier s’ils obtiennent un consensus. / The present thesis describes a multidisciplinary research project on emotion recognition in sounds, covering psychological theories, acoustic-based signal analysis, machine learning and chaotic dynamics.In our social interactions and relationships, we rely greatly on the communication of information and on our perception of the messages transmitted. In fact communication happens when signals transmit information between a source and a destination. The signal can be verbal,and the information is then carried by sound patterns, such as words. In non verbal vocal communication however, information can be perceptual patterns that convey affective cues,that we sense and appraise in the form of intentions, attitudes, moods and emotions.The prevalence of the affective component can be seen in human computer interactions(HCI) where the development of automated applications that understand and express emotions has become crucial. Such systems need to be meaningful and friendly to the end user, so thatour interaction with them becomes a positive experience. Although the automatic recognition of emotions in sounds has received increased attention in recent years, it is still a young fieldof research. Not only does it contribute to Affective Computing in general, but it also provides insight into the significance of sounds in our daily life.In this thesis the problem of affect recognition is addressed from a dual perspective: we start by taking a standard approach of acoustic-based signal analysis, where we survey and experiment with existing features to determine their role in emotion communication. Then,we turn to chaotic dynamics and time series symbolization, to understand the role of the inherent dynamics of sounds in affective expressiveness. We conduct our studies in the context of nonverbal sounds, namely voice, music and environmental sounds.From a human listening point of view, an annotation task is conducted to build a ground truth of nonverbal singing voices, labelled with categorical descriptions of the two-dimensional model of affect. Two types of sounds are included in the study: vocal and glottal.From a psychological perspective, the present research addresses a debate that is of long standing among scientists and psychologists, concerning the common origins of music and voice.The question is addressed from an acoustic-based analysis as well as a nonlinear dynamics approach.From a modeling viewpoint, this work proposes a novel nonlinear dynamics approach for the recognition of affect in sound, based on chaotic dynamics and adaptive time series symbolization.Throughout this thesis, key contrasts in the expressiveness of affect are illustrated among the different types of sounds, through the analysis of acoustic properties, nonlinear dynamics metrics and predictions performances. Finally from a progressive perspective, we suggest that future works investigate features that are motivated by cognitive studies. We also suggest to examine to what extent our features reflect cognitive processes. Additionally we recommend that our dynamic features be tested inlarge scale ER studies through the participation in ER challenges, with an aim to verify if they gain consensus.

xix, 171 p. : ill. (some col.) A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number. / The field of quantum chaos investigates the quantum mechanical behavior of classically chaotic systems. This dissertation begins by describing an experiment conducted on an apparatus constructed to represent a three dimensional analog of a classically chaotic system. Patterns of reflected light are shown to produce fractals, and the behavior of the fractal dimension D F is shown to depend on the light's ability to escape the apparatus. The classically chaotic system is then used to investigate the conductance properties of semiconductor heterostructures engineered to produce a conducting plane relatively free of impurities and defects. Introducing walls that inhibit conduction to partition off sections considerably smaller than the mean distance between impurities defines devices called 'billiards'. Cooling to low temperatures enables the electrons traveling through the billiard to maintain quantum mechanical phase. Exposure to a changing electric or magnetic field alters the electron's phase, leading to fluctuations in the conductance through the billiard. Magnetoconductance fluctuations in billiards have previously been shown to be fractal. This behavior has been charted using an empirical parameter, Q , that is a measure of the resolution of the energy levels within the billiard. The relationship with Q is shown to extend beyond the ballistic regime into the 'quasi-ballistic' and 'diffusive' regimes, characterized by having defects within the conduction plane. A model analogous to the classically chaotic system is proposed as the origin of the fractal conductance fluctuations. This model is shown to be consistent with experiment and to account for changes of fine scale features in MCF known to occur when a billiard is brought to room temperature between low temperature measurements. An experiment is conducted in which fractal conductance fluctuations (FCF) are produced by exposing a billiard to a changing electric field. Comparison of D F values of FCF produced by electric fields is made to FCF produced by magnetic fields. FCF with high D F values are shown to de-correlate at smaller increments of field than the FCF with lower D F values. This indicates that FCF may be used as a novel sensor of external fields, so the response of FCF to high bias voltages is investigated. / Adviser: Stephen Kevan, Chairperson, Physics; Richard Taylor, Advisor, Physics; Robert Zimmerman, Member, Physics; Stephen Gregory, Member, Physics; David Johnson, Outside Member, Chemistry

Le mélange de solutés par les écoulements en milieux poreux contrôle les réactions chimiques dans un grand nombre d'applications souterraines, dont le transport et la remédiation des contaminants, le stockage et l'extraction souterrains d'énergie, et la séquestration du CO2. Nous étudions les mécanismes du mélange à l'échelle du pore et plus précisément comment la topologie de l'écoulement est reliée à la dynamique du mélange d'espèces conservatives; en particulier, l'émergence d'un mélange chaotique est-elle possible dans un milieu poreux tridimensionnel (3D) ? Nous calculons donc numériquement ou mesurons expérimentalement les vitesses d'écoulement et l'évolution temporelle des champs de concentration afin de caractériser la déformation et le mélange à l'échelle du pore. Une première étude, expérimentale, permet de caractériser le mélange dans un fluide s’écoulant à travers un milieu poreux bidimensionnel (2D). Nous mesurons les vitesses par suivi de microparticules solides (''PTV''). L’évolution temporelle de la distance séparant deux particules permet de caractériser la dynamique de la déformation lagrangienne. Des mesures de transport conservatif dans le même milieu fournissent l'évolution temporelle du gradient de concentration moyen (une mesure du mélange). À partir de ces résultats expérimentaux nous proposons la première validation expérimentale à l'échelle du pore de la théorie lamellaire du mélange, reliant les propriétés de la déformation du fluide à la dynamique du mélange. Dans une deuxième étude nous examinons les conditions d'apparition du mélange chaotique dans l’écoulement dans des milieux poreux 3D granulaires ordonnés. Nous effectuons des calculs numériques hautement résolus de d'écoulement de Stokes entre des sphères empilées selon une structure cristalline (cubique simple ou cubique centrée), périodique. La déformation lagrangienne, obtenue à partir des champs de vitesse à l'aide d'outils numériques développés spécifiquement, met en lumière une large variété de dynamiques de la déformation dans ces milieux 3D, selon l'orientation de l'écoulement. Quand la direction de l'écoulement n'est pas normale à l'un des plans de symétrie de réflection du cristal, l'évolution temporelle de la déformation est exponentielle, traduisant une advection chaotique. L’émergence (ou non) du chaos est contrôlée par un mécanisme similaire à la ''transformation du boulanger'': les particules fluides se déplaçant autour d'un grain solide se retrouvent séparées par une surface virtuelle (appelée “variété”) qui émerge de la surface du grain. De multiples variétés existent dans l’écoulement, et la façon dont elles s'intersectent contrôle la nature - chaotique ou non - du mélange, et l'intensité du chaos. En particulier, l'exposant de Lyapunov (une mesure du chaos), est contrôlé par la fréquence spatiale des intersections appropriées à la génération du chaos, nommées ''connections hétéroclinines'' entre variétés. L'image conventionnelle, 2D, des mécanismes du mélange, impose des contraintes topologiques qui ne permettent pas le développement de ces mécanismes 3D. Elle pourrait donc être inadaptée aux milieux poreux naturels. La troisième étude a deux objectifs: (i) fournir une preuve expérimentale de la nature chaotique de l'advection, par la visualisation des variétés et par l'obtention d'une mesure de l'exposant de Lyapunov; et (ii), évaluer si nos résultats numériques obtenus pour des milieux granulaires ordonnés peuvent être généralisés à des milieux désordonnés, plus proches des milieux naturels. L’expérience est fondée sur un empilement désordonné de sphères rendu transparent par l'ajustement optique du liquide avec les sphères. La fluorescence induite par laser (''LIF'') permet de détecter les variétés au sein de l'écoulement, et des techniques PTV de mesurer les vitesses d'écoulement et quantifier l'exposant de Lyapunov. Les premiers résultats expérimentaux sont prometteurs. / Solute mixing in porous media flows plays a central role in driving chemical reactions in a number of subsurface applications, including contaminant transport and remediation, subsurface energy storage and extraction, and CO2 sequestration. We study the mechanisms of solute mixing, in particular how the pore scale flow topology is related to the mixing dynamics of conservative solutes, with a particular emphasis on the possible emergence of chaotic mixing processes in three-dimensional (3D) porous media. To do so, we perform numerical computations or experimental measurements of the flow velocities and temporal evolution of the concentration fields, and characterize fluid deformation and mixing at the pore scale. This PhD work consists of three main studies. In the first study, we experimentally characterize mixing in a fluid flowing through a two-dimensional (2D) porous medium built by lithography. We measure the velocity distributions from Particle Tracking Velocimetry (PTV). The time evolution of the separation distance between two particles is analyzed to characterize the Lagrangian deformation dynamics. In parallel we perform conservative transport experiments with the same porous media, and quantify the temporal evolution of the mean concentration gradient, which is a measure of the mixing rate. From these experimental results we obtain the first experimental pore scale validation of the lamella mixing theory, which relates the fluid deformation properties to the mixing dynamics. In the second study, we investigate the conditions of emergence of chaotic mixing in the flow through 3D ordered granular porous media. In these periodic cubic crystalline packings (Simple Cubic - SC - and Body-Centered Cubic - BCC) of spheres, we are able to perform highly resolved computations of the 3D Stokes flow. Using custom-developed numerical tools to measure the Lagrangian deformation from the computed velocity fields, we uncover the existence of a rich array of Lagrangian deformation dynamics in these 3D media, depending on the flow orientation. When the flow direction is not normal to one of the reflection symmetry planes of the crystalline lattice, we find that the Lagrangian deformation dynamics follow an exponential law, which indicates chaotic advection. This chaotic behavior is controlled by a mechanism akin to the baker's transformation: fluid particles traveling around a solid grain along different paths end up either separated by, or on the same side of, a virtual surface projecting from the grain surface and called a manifold. Multiple such manifolds exist within the flow, and the way they intersect controls the nature of mixing (that is, either non-chaotic or chaotic), and the strength of chaos. We show in particular that the magnitude of the Lyapunov exponent (a measure of the vigor of chaos) is controlled by the spatial frequency of transverse connections between the manifolds (called heteroclinic intersections). We thus demonstrate that the conventional 2D picture of the mechanisms of mixing may not be adapted for natural porous media because that picture imposes topological constraints which cannot account for these important 3D mechanisms. The third study has two objectives: (i) provide experimental evidence of the chaotic nature of pore scale advection/mixing, both by visualizing the manifolds and by obtaining a quantitative estimate of the Lyapunov exponent; and (ii) assess if the results obtained numerically in ordered packings of spheres extend to random packings, which are closer to natural porous media. The experiment features a random packing of glass beads rendered transparent by optical index-matching between the fluid and solid grains. We use Laser Induced Fluorescence (LIF) to detect the manifolds, and PTV techniques to measure flow velocities and subsequently quantify Lyapunov exponent. The first experimental results are promising.

Para qualquer sistema observado, físico ou qualquer outro, geralmente se deseja fazer predições para sua evolução futura. Algumas vezes, muito pouco é conhecido sobre o sistema. Se uma série temporal é a única fonte de informação no sistema, predições de valores futuros da série requer uma modelagem da lei da dinâmica do sistema, talvez não linear. Um interesse em particular são as capacidades de previsão do modelo global para análises de séries temporais. Isso pode ser um procedimento muito complexo e computacionalmente muito alto. Nesta dissertação, nos concetraremos em um determinado caso: Em algumas situações, a única informação que se tem sobre o sistema é uma série sequencial de dados (ou série temporal). Supondo que, por detrás de tais dados, exista uma dinâmica de baixa dimensionalidade, existem técnicas para a reconstrução desta dinâmica.O que se busca é desenvolver novas técnicas para poder melhorar o poder de previsão das técnicas já existentes, através da programação computacional em Maple e C/C++.

Submitted by DANIELE ALESSANDRA REGHINI GAZETTA null (daniellygaze@hotmail.com) on 2016-01-15T17:36:23Z No. of bitstreams: 1 diss-daniele.pdf: 783553 bytes, checksum: e593f1ebb872fff02a080d05283744d5 (MD5) / Rejected by Ana Paula Grisoto (grisotoana@reitoria.unesp.br), reason: Solicitamos que realize uma nova submissão seguindo as orientações abaixo: No campo “Versão a ser disponibilizada online imediatamente” foi informado que seria disponibilizado o texto completo porém no campo “Data para a disponibilização do texto completo” foi informado que o texto completo deverá ser disponibilizado apenas 6 meses após a defesa. Caso opte pela disponibilização do texto completo apenas 6 meses após a defesa selecione no campo “Versão a ser disponibilizada online imediatamente” a opção “Texto parcial”. Esta opção é utilizada caso você tenha planos de publicar seu trabalho em periódicos científicos ou em formato de livro, por exemplo e fará com que apenas as páginas pré-textuais, introdução, considerações e referências sejam disponibilizadas. Se optar por disponibilizar o texto completo de seu trabalho imediatamente selecione no campo “Data para a disponibilização do texto completo” a opção “Não se aplica (texto completo)”. Isso fará com que seu trabalho seja disponibilizado na íntegra no Repositório Institucional UNESP. Por favor, corrija esta informação realizando uma nova submissão. Agradecemos a compreensão. on 2016-01-15T19:12:27Z (GMT) / Submitted by DANIELE ALESSANDRA REGHINI GAZETTA null (daniellygaze@hotmail.com) on 2016-01-16T16:43:56Z No. of bitstreams: 2 diss-daniele.pdf: 783553 bytes, checksum: e593f1ebb872fff02a080d05283744d5 (MD5) daniele-dissert.pdf: 585710 bytes, checksum: 222237614b39411bc9b9a3e82ad6ab17 (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2016-01-18T16:33:44Z (GMT) No. of bitstreams: 1 gazetta_dar_me_sjrp.pdf: 783553 bytes, checksum: e593f1ebb872fff02a080d05283744d5 (MD5) / Made available in DSpace on 2016-01-18T16:33:44Z (GMT). No. of bitstreams: 1 gazetta_dar_me_sjrp.pdf: 783553 bytes, checksum: e593f1ebb872fff02a080d05283744d5 (MD5) Previous issue date: 2016-01-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O principal resultado dessa dissertação é o Teorema de Poincaré-Bendixson para campos de vetores planares suaves por partes, que nos diz quais são os tipos de conjuntos limite. Estudaremos também detalhes a respeito dos conceitos de conjuntos minimais e caóticos em campos de vetores planares suaves por partes. / The main result of this work is the Poincaré - Bendixson Theorem for planar piecewise smooth vector fields, which tell us what kind of limit sets arise in this context. We will also study details about the concepts of minimal and chaotic sets in planar piecewise smooth vector fields.

Para qualquer sistema observado, físico ou qualquer outro, geralmente se deseja fazer predições para sua evolução futura. Algumas vezes, muito pouco é conhecido sobre o sistema. Se uma série temporal é a única fonte de informação no sistema, predições de valores futuros da série requer uma modelagem da lei da dinâmica do sistema, talvez não linear. Um interesse em particular são as capacidades de previsão do modelo global para análises de séries temporais. Isso pode ser um procedimento muito complexo e computacionalmente muito alto. Nesta dissertação, nos concetraremos em um determinado caso: Em algumas situações, a única informação que se tem sobre o sistema é uma série sequencial de dados (ou série temporal). Supondo que, por detrás de tais dados, exista uma dinâmica de baixa dimensionalidade, existem técnicas para a reconstrução desta dinâmica.O que se busca é desenvolver novas técnicas para poder melhorar o poder de previsão das técnicas já existentes, através da programação computacional em Maple e C/C++.

Estudamos nesta dissertação o tempo de recorrência em sistemas dinâmicos, concentrando-nos na estatística do tempo de retorno. Calculamos numericamente a distribuição de tempo de retorno a uma região específica do espaço de fases de sistemas caóticos e comparamos com a distribuição binomial, deduzida para um processo aleatório. Os principais resultados obtidos foram: surgimento do efeito que denominamos memória de curto alcance, típico de sistemas determinísticos e associado à distribuição das órbitas periódicas instáveis; a distribuição de tempo de retorno caracteriza as principais propriedades temporais no caso de sistemas intermitentes. As conexões do tempo de retorno com regimes de transporte anômalo foram apresentadas, ressaltando suas limitações. O tempo de retorno foi utilizado ainda para analisar séries temporais, obtidas tanto de um modelo de mistura de um contaminante escalar passivo, como experimentalmente no plasma confinado magnéticamente. No primeiro caso constatamos que os retornos da série temporal assemelham-se às recorrências no espaço de fases do sistema dinâmico responsável pela mistura do contaminante: o mapa padrão com fase aleatória. Constatamos o surgimento de caudas de lei de potência na distribuição de tempo de retorno e calculamos sua dependência com o aumento da não linearidade e da aleatoriedade do sistema. Destacamos o efeito de múltiplas caudas de lei de potência, ausente no caso das distribuições obtidas no espaço de fases. Às séries obtidas em Tokamaks aplicamos o modelo de cascata log-normal para explicar sua função densidade de probabilidade. A distribuição de tempo de retorno destas séries mostrou estar diretamente relacionada com a correlação de curto e longo alcance presente na série. / We study the recurrence time in dynamical systems. The statistics of the recurrence time to a specific region of the phase space of chaotic dynamical systems were obtained numerically and compared with the binomial-like distribution, deduced for a random process. The main results are: the presence of the so called short time memory effect, typical for deterministic systems and related to the distribution of the unstable periodic orbits; the return time distribution captures the main temporal properties of intermittent systems. The possible connections of the recurrence time statistics to the anomalous transport were presented, with special attention to their limitations. The return time statistics was applied to analyze time series obtained from an Hamiltonian model and from magnetically confined plasma. In the first case we noticed that the recurrences of the series were similar to the recurrences obtained in the phase space of the Hamiltonian dynamical system: the standard map with a random phase. We analyze the dependence of the power-law tails of the distributions with the non-linearity and with the randomness of the system. One effect that appears only in the time series case is the multiple power law tails. We apply the log-normal cascade model to explain the probability density function of the series obtained in Tokamaks. The recurrence time statistics of the series is closely related to the short and long time correlation present on the series.