A análise de sistemas dinâmicos não lineares pode ser baseada em séries obtidas de modelos matemáticos ou de experimentos. Modelos matemáticos para respostas aeroelásticas associadas ao estol dinâmico são muito difíceis de obter. Neste caso, experimentos e ensaios em vôo parecem fornecer uma base mais apropriada para a análise da dinâmica não linear. Técnicas de sistemas dinâmicos baseadas em análise de séries temporais podem ser aplicadas para a aeroelasticidade não linear. Quando tem-se disponível apenas séries experimentais, as técnicas de reconstrução do espaço de estados têm sido extensivamente utilizadas. Além disso, os expoentes de Lyapunov fornecem uma caracterização qualitativa e quantitativa do comportamento caótico de sistemas não lineares, assim, um expoente de Lyapunov positivo é um forte indicativo de caos. Medidas de entropia também fornecem informações importantes da complexidade do sistema não linear, consequentemente sua aplicação às séries temporais aeroelásticas representam uma forma apropriada para identificar movimentos caóticos. Este trabalho apresenta a aplicação de técnicas da análise de séries temporais, tais como, reconstrução do espaço de estados, expoentes de Lyapunov e medidas de entropia para respostas aeroelásticas não lineares para prever o comportamento caótico. Um modelo de asa flexível foi construído e testado em túnel de vento de circuito fechado com velocidade do escoamento variando entre 9,0 e 17,0 m/s. O modelo foi montado sobre uma plataforma giratória que produzia variações no ângulo de incidência. Deformações estruturais foram capturadas por meio de extensômetros que forneciam informações da resposta aeroelástica. O método da defasagem é utilizado para reconstruir o espaço de estados das séries temporais obtidas no experimento. Para obter a defasagem utilizada na reconstrução foi usada a análise da função de autocorrelação. Para determinar a dimensão do atrator é calculada a integral de correlação. A evolução do espectro de frequências e do espaço de estados reconstruído é analisada com as variações da velocidade do escoamento e da frequência de oscilação da plataforma. Os expoentes de Lyapunov e a entropia de Rényi foram obtidos para identificar o comportamento caótico. Os resultados foram analisados com a variação da velocidade do escoamento e da frequência de oscilação da plataforma. As técnicas utilizadas foram eficientes para observar o aparecimento de mudanças no sistema e do comportamento caótico com uma escala de interação fluido-estrutura complexa para movimentos com altos ângulos de incidência. / The analysis of non-linear dynamical systems can be based on data from either a mathematical model or an experiment. Mathematical models for aeroelastic response associated to the dynamic stall behavior are very hard to obtain. In this case, experimental or in flight data seems to provide suitable basis for non-linear dynamical analysis. Dynamic systems techniques based on time series analysis can be adequately applied to non-linear aeroelasticity. When experimental data are available, state space reconstruction methods have been widely considered. Moreover, the Lyapunov exponents provides qualitative and quantitative characterization of nonlinear systems chaotic behavior, since positive Lyapunov exponent is a strong signature of chaos. Entropy measures also provide important information on the complexity of nonlinear system, therefore its application to aeroelastic time series represent a proper way to seek for chaotic motions. This work presents the application techniques from time series analysis, such as, state space reconstruction, Lyapunov exponents and entropy measures to nonlinear aeroelastic responses, in order to predict chaotic behavior. A flexible wing model has been constructed and tested in a closed circuit wind tunnel with freestream between 9,0 and 17,0 m/s. The wing model has been mounted on a turntable that allows variations to the wing incidence angle. Structural deformation is captured by means of strain gages, thereby providing information on the aeroelastic response. The method of delays has been used to identify an embedded attractor in the state space from experimentally acquired aeroelastic response time series. To obtain the time delay value to manipulate the time series during reconstruction, the autocorrelation function analysis has been used. For the attractor embeeding dimension calculation the correlation integral approach has been considered. The evolution of frequency spectra and the reconstrueted state space is analyzed for variations of the freestream and the frequency of oscilIation of the turntable. Lyapunov exponents and Rényi entropy have been achieved in order to seek for chaotic behavior. The results were analyzed with the variation of the freestream and the frequency of oscillation of the turntable. The used techniques had been efficient to observe the occurence of changes and chaotic behavior withim a range of complex fluid-structure interaction at higher angle of incidence motions.

O principal objetivo do presente trabalho é propor, desenvolver, testar e apresentar um método para a classificação do grau de desenvolvimento da capacidade cognitiva espacial de diferentes indivíduos. 37 alunos de graduação tiveram seus eletroencefalogramas (EEGs) capturados enquanto estavam engajados em tarefas de rotação mental de imagens tridimensionais. Seu grau de desenvolvimento da capacidade cognitiva espacial foi avaliado utilizando-se um teste psicológico BPR-5. O maior expoente de Lyapunov (LLE) foi calculado a partir de cada um dos 8 canais dos EEGs capturados. OS LLEs foram então utilizados como tuplas de entrada para 5 diferentes classificadores: i) perceptron de múltiplas camadas, ii) rede neural artificial de funções de base radial, iii) perceptron votado, iv) máquinas de vetor de suporte, e v) k-vizinhos. O melhor resultado foi obtido utilizando-se uma RBF com 4 clusters e a função de kernel Puk. Também foi realizada uma análise estatística das diferenças de atividade cerebral, baseando-se nos LLEs calculados, entre os dois grupos de interesse: SI+ (indivíduos com um suposto maior grau de desenvolvimento da sua capacidade cognitiva espacial) e SI- (grupo de controle) durante a realização de tarefas de rotação mental de imagens tridimensionais. Uma diferença média de 16% foi encontrada entre os dois grupos. O método de classificação proposto pode vir a contribuir e a interagir com outros processos na analise e no estudo da capacidade cognitiva espacial humana, assim como no entendimento da inteligência humana como um todo. Um melhor entendimento e avaliação das capacidades cognitivas de um indivíduo podem sugerir a este elementos de motivação, facilidade ou de inclinações naturais suas, podendo, provavelmente, afetar as decisões da sua vida e carreira de uma forma positiva. / The main objective of the present work is to propose, develop, test, and show a method for classifying the spatial cognition degree of development on different individuals. Thirty-Seven undergraduate students had their electroencephalogram (EEG) recorded while engaged in 3-D images mental rotation tasks. Their spatial cognition degree of development was evaluated using a BPR-5 psychological test. The Largest Lyapunov Exponent (LLE) was calculated from each of the 8 electrodes recorded in each EEG. The LLEs were used as input for five different classifiers: i) multi-layer perceptron artificial neural network, ii) radial base functions artificial neural network, iii) voted perceptron artificial neural network, iv) support vector machines, and v) K-Nearest Neighbors. The best result was achieved by using a RBF with 4 clusters and Puk kernel function. Also a statistical analysis of the brain activity, based in the calculated LLEs, differences between two interest groups: SI+ (participants with an alleged higher degree of development of their spatial cognition) and SI- (control group) during the performing of mental rotation of tridimensional images tasks was done.. An average difference of 16% was found between both groups. The proposed classification method can contribute and interact with other processes in the analysis and study of human spatial cognition, as in the understanding of the human intelligence at all. A better understanding and evaluation of the cognitive capabilities of an individual could suggest him elements of motivation, ease or natural inclinations, possibly affecting the decisions of his life and carrier positively.

Orientador: Patricio A. Letelier Sotomayor / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-13T05:26:41Z (GMT). No. of bitstreams: 1 Steklain_AndreFabiano_D.pdf: 11096709 bytes, checksum: 482e5ffb56f964f7786da54ec1791864 (MD5) Previous issue date: 2009 / Resumo: Neste trabalho a dinâmica do problema de Hill é analisada utilizando-se duas metodologias diferentes. Na primeira metodologia, ainda no contexto da mecânica newtoniana, utilizamos potenciais que reproduzem efeitos da relatividade geral. Foram utilizados os potenciais de Paczynski-Wiita e um dos potenciais de Artemova, Bjornsson e Novikov (ABN). Estes potenciais reproduzem os efeitos que surgem no contexto da métrica de Schwarzschild (horizonte de eventos) e da métrica de Kerr (efeito Lense-Thirring), respectivamente. Na segunda metodologia as equações de movimento são obtidas a partir da relatividade geral, utilizando a métrica aproximada de um sistema binário obtida a partir de uma expansão pós-newtoniana de primeira ordem (1PN). A análise da dinâmica envolveu o estudo da estabilidade das órbitas fechadas, utilizando ferramentas clássicas como seções de Poincaré e expoentes de Lyapunov. Foram estudadas também trajetórias não limitadas utilizando escape fractal. Dentre os resultados obtidos destacam-se dois fatos. No caso do potencial ABN, existe uma influência da rotação na estabilidade das órbitas. No caso relativístico existe um limite para o qual o sistema, em geral caótico, se torna estável, diferentemente do que se poderia esperar de acordo com os potenciais pseudo-Newtonianos, em particular considerando o potencial de Paczynski-Wiita. / Abstract: In this work the Hill problem dynamics is analyzed using two different approaches. In the first approach, still in the realm of Newtonian mechanics, we use potentials that reproduce General Relativity effects. We use the Paczynski-Wiita and one of the Artemova, Bj¨ornsson e Novikov (ABN) potentials. These potentials reproduce effects that arise in the context of the Schwarzschild metric (event horizon) and of the Kerr metric (Lense-Thirring effect), respectively. On the second approach the equations of motion are obtained using general relativity, from the approximate metric of a binary system obtained from post-Newtonian expansions up to first order (1PN). In the analysis of the dynamics we study the stability of bounded orbits using classical tools, like Poincare sections and Lyapunov exponents. We also study open trajectories using Fractal Escape analysis. From our results we remark that two features. For the ABN potential there is an influence of the rotations on the stability of the orbits. In general relativity there is a limit where the system, in general chaotic, become stable, in disagreement with the pseudo-Newtonian potentials, in particular the Paczy'nski-Wiita potential. / Doutorado / Doutor em Matemática Aplicada

Orientadores: José Raimundo de Oliveira, Ignacio Bravo Muñoz / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Elétrica e de Computação / Made available in DSpace on 2018-08-21T12:37:43Z (GMT). No. of bitstreams: 1 Fazanaro_FilipeIeda_D.pdf: 53323687 bytes, checksum: 76694b226ed99a337ecee1769ed9c4e0 (MD5) Previous issue date: 2012 / Résumén: Esta tesis tiene como objetivo la caracterización de sistemas dinámicos no lineales y abruptos. Se propone una nueva metodología para la estimación del espectro de Lyapunov capaz de superar las dificultades relacionadas en los sistemas basados en funciones lineales por partes sobre la aplicación de los métodos clásicos de cálculo (cuando se utiliza linealización local o análisis de series de las series temporales experimentales). Este enfoque, denominado como Dinámica de los Clones, realiza la estimación del espectro de Lyapunov y también mejora el estudio de las características topológicas relacionadas con los procesos de mezcla que dan lugar al comportamiento caótico. Este estudio se lleva a cabo utilizando las Estructuras Coherentes de Lagrange que pueden obtenerse a través de la construcción de un campo de Exponentes de Lyapunov de Tiempo Finito donde se puede identificar a las crestas (o las separatrices) que dan la posibilidad de identificar las distintas regiones de convergencia y divergencia del espacio de estados. Debido al hecho que esta tesis se desarrolla fundamentalmente bajo un ordenador, los aspectos prácticos involucrados en los experimentos numéricos necesarios, emplean algunos conceptos y herramientas de computación en paralelo. Esto último permitió la optimización de los algoritmos implementados. Por lo tanto, los experimentos se realizaron para verificar la eficacia del enfoque de las Dinámicas Clonadas para la caracterización del circuito de Chua, y también para obtener las Estructuras Coherentes de Lagrange que tienen relación con los modelos dinámicos capaces de generar atractores caóticos multiscroll / Resumo: Essa tese objetiva caracterizar sistemas dinâmicos não lineares não suaves. Para tal, é proposta uma nova abordagem de estimação do espectro de Lyapunov capaz de contornar as dificuldades intrínsecas aos sistemas estruturados por funções lineares por partes quando da aplicação de metodologias clássicas (baseadas em linearizações locais ou em análises de séries temporais). Essa abordagem possibilita a estimação do espectro de Lyapunov e, além disso, auxilia no estudo das características topológicas relacionadas aos processos de mistura que dão origem ao comportamento caótico. Essa linha de estudo é realizada através das Estruturas Lagrangianas Coerentes, as quais são obtidas pela construção de um campo de Expoentes de Lyapunov de Tempo Finito, onde é possível identificar cristas (ou separatrizes) que dividem regiões de convergência e de divergência no espaço de estados. Por se tratar de um trabalho basicamente computacional, essa tese contempla os aspectos práticos envolvidos para a realização dos experimentos numéricos através da utilização de alguns conceitos e ferramentas de computação paralela, o que possibilitou a otimização dos algoritmos implementados. Nesse sentido, os experimentos foram realizados de modo a verificar a eficácia da metodologia proposta para a caracterização do circuito de Chua e, ainda, foram obtidas as Estruturas Lagrangianas Coerentes para os modelos dinâmicos capazes de gerar atratores caóticos multiscroll / Abstract: This thesis aims to characterize non-smooth nonlinear dynamical systems. To accomplish this purpose, we propose a new approach for estimating the Lyapunov spectrum which is capable to overcome the intrinsic difficulties of classical methods (based on local linearization or time series analysis) when dealing with systems based on piecewise linear functions. This approach, called Cloned Dynamics, allows the estimation of the Lyapunov spectrum and also improves the study of the topological features related to the mixing processes that give rise to the chaotic behavior. This study is performed using the Lagrangian Coherent Structures which are obtained by the construction of a Finite Time Lyapunov Exponents field where it is possible to identify the ridges (or the separatrices) which divide the convergence and divergence regions of the state space. Due to the fact that this thesis is basically developed under a computer environment, the practical features involved in the numerical experiments employing some parallel computing concepts and tools are discussed, which allowed the optimization of the algorithms implemented. In this sense, experiments were performed to verify the effectiveness of the Cloned Dynamics approach for the characterization of the Chua's circuit, and also to obtain the Lagrangian Coherent Structures related to the dynamical models capable of generating multiscroll chaotic attractors / Doutorado / Automação / Doutor em Engenharia Elétrica

Orientador: Luiz Antonio Barrera San Martin / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-21T17:52:11Z (GMT). No. of bitstreams: 1 Ferraiol_ThiagoFanelli_D.pdf: 1248936 bytes, checksum: b0a3aefba1736bb7ff7be29e982d7aa0 (MD5) Previous issue date: 2012 / Resumo: Nesta tese apresentamos resultados que fornecem a regularidade dos expoentes de Lyapunov com uma abordagem via teoria de Lie. A generalização dos expoentes de Lyapunov para fluxos em fibrados flag associados a um fibrado principal é utilizada para obter a diferenciabilidade de certas combinações lineares do espectro de Lyapunov. Essas combinações que são diferenciáveis são determinadas a partir da caracterização da decomposição de Morse mais fina do fluxo nos fibrados flag. A diferenciabilidade é tomada com repeito à perturbação do fluxo por elementos do grupo de calibre do fibrado principal / Abstract: In this thesis we present results about regularity of Lyapunov Exponents via a Lie Theory approach. The generalization of Lyapunov Exponents for flows in flag bundles is used to obtain the differenciability of certain linear combinations of the Lyapunov spectra. This specific combinations that are differentiable are determined by the caracterization of the finest Morse decomposition of the flows on flag bundles. The differenciability is taken with respect to the perturbation of the flow by elements in the gauge group of the principal bundle / Doutorado / Matematica / Doutor em Matemática

L'augmentation des performances des futurs systèmes dynamiques nécessite la prise en compte des phénomènes physiques non linéaires. Cette thèse apporte un éclairage et des contributions sur deux sujets complémentaires liés aux phénomènes dynamiques non linéaires. Le mémoire de thèse est divisé en deux parties.La première partie porte sur les non-linéarités des amplificateurs de puissance dans le cadre d'applications destinées aux télécommunications ou à la diffusion audio-visuelle. Plusieurs méthodes de modélisation et de linéarisation des amplificateurs de puissance ont été conçues et discutées. Un banc de test a été développé afin d'évaluer les méthodes sur des amplificateurs réels. La robustesse de ces techniques à un mauvais alignement temporel des signaux ainsi que leur capacité à faire face à des artefacts spectraux ont été évaluées. Par ailleurs, nous avons effectué une étude théorique sur l'existence et la prise en compte de solutions multiples dans l'approche adaptative par apprentissage indirect. La deuxième partie traite des systèmes dynamiques non linéaires qui présentent des solutions chaotiques. Ces systèmes sont bien connus, mais les techniques d'identification de ces solutions manquent de fiabilité ou nécessitent une puissance de calcul importante. Dans cette thèse, plusieurs méthodes utilisant également le calcul parallèle sont présentées. Les systèmes à commande différentielle fractionnaire sont brièvement discutés. Il est aussi montré, qu'il existe des systèmes liés à des fonctions de transfert non linéaires avec quantification pour lesquels les méthodes d'analyse classiques échouent / In order to achieve better performance of modern communication devices, that have to be operated on its physical limits, the nonlinear phenomena need to be taken into the account. This thesis brings insight into two different subjects related with nonlinear dynamical phenomena. The thesis itself is divided into two parts : the first part is focused on the domain of nonlinear power amplifiers from the system point of view. Several methods for modelization and linearization of power amplifiers have been designed and discussed. A test-bench has been assembled in order to evaluate the proposed methods on real power amplifiers. Then the robustness to time misalignment in the system and the ability to deal with spectral artifacts in the system of presented methods have been evaluated. Also a theoretical study has been conducted on the existence and management of multiple solutions in the frame of adaptive indirect learning approach. The second part deals with nonlinear dynamical systems that are exhibiting chaotic solutions. Such systems are well known, but techniques for identifying reliable such solutions are either missing or are computational intense. In this thesis several methods using also parallel computing are presented. Systems with fractional differential order are briefly discussed. It is as well shown, that there exists systems related with quantified nonlinear transfer functions for which the standard analyzing methods fails

The master's thesis deals mainly with continuous nonlinear dynamical systems that exhibit chaotic behavior. The main goal is to create algorithms for chaos detection and their subsequent testing on known models. Most of the thesis is devoted to the estimation of the Lyapunov exponents, further it deals with the estimation of the fractal dimension of an attractor and summarizes the 0--1 test. The thesis includes three algorithms created in MATLAB -- an algorithm for estimating the largest Lyapunov exponent and two algorithms for estimating the entire Lyapunov spectra. These algorithms are then tested on five continuous dynamical systems. Especially the error of estimation, speed of these algorithms and properties of Lyapunov exponents in different areas of system behavior are investigated.

Diplomová práce pojednává o chaotických dynamických systémech se zvláštním zaměřením na jejich synchronizaci. Proces synchronizace je aplikován použitím dvou různých metod, a to - metodou úplné synchronizace na dva Lorenzovy systémy a metodou negativní zpětné vazby na dva Rösslerovy systémy. Dále je prozkoumána možná aplikace synchronizace chaotických systémů v oblasti soukromé komunikace, která je doplněná algoritmy v prostředí MATLAB.

In this thesis the Lyapunov exponents of random dynamical systems are presented and investigated. The main results are: 1. In the space of all unbounded linear cocycles satisfying a certain integrability condition, we construct an open set of linear cocycles have simple Lyapunov spectrum and no exponential separation. Thus, unlike the bounded case, the exponential separation property is nongeneric in the space of unbounded cocycles. 2. The multiplicative ergodic theorem is established for random difference equations as well as random differential equations with random delay. 3. We provide a computational method for computing an invariant measure for infinite iterated functions systems as well as the Lyapunov exponents of products of random matrices. / In den vorliegenden Arbeit werden Lyapunov-Exponented für zufällige dynamische Systeme untersucht. Die Hauptresultate sind: 1. Im Raum aller unbeschränkten linearen Kozyklen, die eine gewisse Integrabilitätsbedingung erfüllen, konstruieren wir eine offene Menge linearer Kyzyklen, die einfaches Lyapunov-Spektrum besitzen und nicht exponentiell separiert sind. Im Gegensatz zum beschränkten Fall ist die Eingenschaft der exponentiellen Separiertheit nicht generisch in Raum der unbeschränkten Kozyklen. 2. Sowohl für zufällige Differenzengleichungen, als auch für zufällige Differentialgleichungen, mit zufälligem Delay wird ein multiplikatives Ergodentheorem bewiesen. 3.Eine algorithmisch implementierbare Methode wird entwickelt zur Berechnung von invarianten Maßen für unendliche iterierte Funktionensysteme und zur Berechnung von Lyapunov-Exponenten für Produkte von zufälligen Matrizen.

Human movement is inherently complex, requiring the control and coordination of many neurophysiological and biomechanical degrees-of-freedom, and the extent to which individuals exhibit variation in their movement patterns is captured by the construct of motor variability (MV). MV is being used increasingly to describe movement quality and function among clinical populations and elderly individuals. However, current evidence presents conflicting views on whether increased MV offers benefits or is a hindrance to performance. To better understand the utility of MV for performance prediction, we focused on current research needs in the military domain. Dismounted soldiers, in particular, are expected to perform at a high level in complex environments and under demanding physical conditions. Hence, it is critical to understand what strategies allow soldiers to better adapt to fatigue and diverse environmental factors, and to develop predictive tools for estimating changes in soldier performance. Different aspects of performance such as motor learning, experience, and adaptability to fatigue were investigated when soldiers performed various gait tasks, and gait variability (GV) was quantified using four different types of measures (spatiotemporal, joint kinematics, detrended fluctuation analysis, and Lyapunov exponents). During a novel obstacle course task, we found that frontal plane coordination variability of the hip-knee and knee-ankle joint couples exhibited strong association with rate of learning the novel task, explaining 62% of the variance, and higher joint kinematic variability during the swing phase of baseline gait was associated with faster learning rate. In a load carriage task, GV measures were more sensitive than average gait measures in discriminating between experience and load condition: experienced cadets exhibited reduced GV (in spatiotemporal measures and joint kinematics) and lower long-term local dynamic stability at the ankle, compared to the novice group. In the final study investigating multiple measures of obstacle performance, and variables predictive of changes in performance following intense whole-body fatigue, joint kinematic variability of baseline gait explained 28-59% of the variance in individual performances changes. In summary, these results support the feasibility of anticipating and augmenting task performance based on individual motor variability. This work also provides guidelines for future research and the development of training programs specifically for improving military training, performance prediction, and performance enhancement. / Doctor of Philosophy / All people move with some level of inherent variability, even when doing the same activity, and the extent to which individuals exhibit variation in their movement patterns is captured by the construct of motor variability (MV). MV is being increasingly used to describe movement quality and function among clinical populations and elderly individuals. However, it is still unclear whether increased MV offers benefits or is a hindrance to performance. To better understand the utility of MV for performance prediction, we focused on current research needs in the military domain. Dismounted soldiers, in particular, are expected to perform at a high level in complex environments and under demanding physical conditions. Hence, it is critical to understand what strategies allow soldiers to better adapt to fatigue and diverse environmental factors, and to develop tools that might predict changes in soldier performance. Different aspects of performance were investigated, including learning a new activity, experience, and adaptability to fatigue, and gait variability was quantified through different approaches. When examining how individual learn a novel obstacle course task, we found that certain aspects of gait variability had strong associations with learning rate. In a load carriage task, variability measures were determined to be more sensitive to difference in experience level and load condition compared to typical average measures of gait. Specifically, variability increased with load, and the experienced group was less variable overall and more stable in the long term. Lastly, a subset of gait variability measures were associated with individual differences in fatigue-related changes in performance during an obstacle course. In summary, the results presented here support that it may be possible to both anticipate and enhance task performance based on individual variability. This work also provides guidelines for future research and the development of training programs specifically for improving military training, performance prediction, and performance enhancement.