Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-10-10T18:52:25Z No. of bitstreams: 1 DESIANE MAIARA GOMES DOS SANTOS – DISSERTAÇÃO (PPGFísica) 2015.pdf: 6011160 bytes, checksum: a5021549766593cfe2eb8fe5314ea39b (MD5) / Made available in DSpace on 2018-10-10T18:52:25Z (GMT). No. of bitstreams: 1 DESIANE MAIARA GOMES DOS SANTOS – DISSERTAÇÃO (PPGFísica) 2015.pdf: 6011160 bytes, checksum: a5021549766593cfe2eb8fe5314ea39b (MD5) Previous issue date: 2015-04-10 / Capes / Nesta dissertação, analisamos a dinâmica de osciladores parametricamente forçados, com enfoque na amplificação de pequenos sinais. Iniciamos por uma revisão da ressonância paramétrica e da amplificação paramétrica em um oscilador linear parametricamente excitado. Em seguida, estudamos dois tipos de osciladores não-lineares parametricamente forçados e concluímos a dissertação com a análise de um dímero parametricamente excitado. Basicamente, analisamos os fenômenos de ressonância paramétrica e de amplificação paramétrica, comparando os resultados obtidos analiticamente (via métodos da média ou do balanço harmônico) com os obtidos via integração numérica das equações do movimento. Em todos os casos, obtivemos a linha de transição para a instabilidade paramétrica do oscilador paramétrico. Nós excitamos os amplificador paramétrico com e sem dessintonia entre entre o bombeamento e o sinal externo ac. Verificamos que o ganho da amplificação paramétrica depende da sensitivamente na fase do sinal externo ac e na amplitude do bombeamento. Mostramos que tais sistemas podem ser facilmente utilizados para recepção e decodificação de sinais com modulação de fase. Além disso, obtivemos séries temporais, envelopes e transformadas de Fourier para a resposta da amplificação paramétrica de pequenos sinais ac. Especificamente nos casos dos osciladores de Duffing parametricamente forçados, obtivemos e analisamos linhas de bifurcação e a amplitude dos ciclos limites como função da frequência e da amplitude de bombeamento. Adicionalmente, conseguimos obter uma relação analítica para os ganhos do sinal e do idler dos osciladores não-lineares parametricamente forçados pelo método do balanço harmônico. Os resultados obtidos implicam que os amplificadores paramétricos não-lineares podem ser excelentes detectores, especialmente em pontos próximos a bifurcações para instabilidade, em que apresentam altos ganhos e largura de banda bem estreitas. Por último, investigamos também o comportamento de dois osciladores lineares acoplados e parametricamente estimulados, com e sem força externa ac. Tais sistemas são muito sensíveis à fase do sinal a ser amplificado e podem ser utilizados para criar amplificadores sintonizáveis em função do parâmetro de acoplamento. / In this dissertation, we studied the dynamics of parametrically-driven oscillators, with a focus on the amplification of small signals. We begin with a revision of parametric resonance and parametric amplification in a linear oscillator parametrically excited. Next, we studied two types of nonlinear parametrically-driven oscillators and finished the dissertation with an analysis of a parametric dimer. Basically, we analyzed the phenomena of parametric resonance and parametric amplification by comparing the results obtained analytically (via the averaging or harmonic balance methods) with those of numerical integration of the equations of motion. In all cases, we obtained the transition line to parametric instability of the parametric oscillator. We excited the parametric amplifier with and without detuning between the pump and the external signal. We found that the parametric amplification depends sensitively on the phase of the external ac signal and on the internal pump amplitude. We showed that such amplifiers can be easily used for the reception and decoding of signals with phase modulation. Furthermore, we obtained time series, envelopes, and Fourier transforms of the response of the parametric amplifier to small external ac signals. Specifically in the cases of the parametrically-driven Duffing oscillators, we obtained and analysed the bifurcation lines and the amplitude of limit cycles as function of the pump amplitude and frequency. In addition, we derived an expression for the signal and idler gains of the nonlinear parametrically-driven oscillators with the harmonic balance method. The results imply that the nonlinear parametric amplifiers can be excellent detectors, specially near bifurcations to instability, due to their high gains and narrow bandwidths. Finally, we studied the dynamics of two linear oscillators coupled and parametrically excited, with and without external ac driving. We found that such systems have a wealth of dynamical responses. They present parametric amplification that is dependent on the coupling parameter and on the phases of the external ac signals. Such systems may be used as tunable amplifiers.

Submitted by RUBENS PAZIM CARNEVAROLLO JUNIOR null (pazim@ufmt.br) on 2016-09-06T21:16:47Z No. of bitstreams: 1 Tese_Pazim_Buzzi.pdf: 1680950 bytes, checksum: 095b9843312f8b0b7449972896a94d73 (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2016-09-09T19:56:44Z (GMT) No. of bitstreams: 1 carnevarollojunior_rp_dr_sjrp.pdf: 1680950 bytes, checksum: 095b9843312f8b0b7449972896a94d73 (MD5) / Made available in DSpace on 2016-09-09T19:56:44Z (GMT). No. of bitstreams: 1 carnevarollojunior_rp_dr_sjrp.pdf: 1680950 bytes, checksum: 095b9843312f8b0b7449972896a94d73 (MD5) Previous issue date: 2016-08-26 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Este trabalho está relacionado ao estudo de bifurcações e órbitas periódicas de sistemas diferenciais suaves por partes planares em duas e três zonas. Em sistemas com duas zonas, estamos interessados em encontrar uma fronteira de separação para um dado par de sistemas suaves de tal modo que o sistema descontínuo, formado pelo par de sistemas suaves, tem um contínuo de órbitas periódicas. Neste caso, denominamos a fronteira de separação como Fronteira de Centros. Para os sistemas com três zonas, consideramos sistemas lineares por partes contínuo, em que a zona central é degenerada e na qual o determinante da parte linear é nulo. Ao mover um parâmetro específico, detectamos algumas bifurcações até então desconhecidas, exibindo transição de salto nos pontos de equilíbrios e o aparecimento de ciclos limites. Em particular, introduzimos a bifurcação Bainha de Espada, caracterizada pelo nascimento de um ciclo limite de um contínuo de pontos de equilíbrios. / This work is related to the study of bifurcations and periodic orbits in planar piecewise smooth differential systems with two and three zones. In the systems with two zones, we are interested in finding a separation boundary for a given pair of smooth systems in such a way that the discontinuous system, formed by the pair of smooth systems, has a continuum of periodic orbits. In this case we call the separation boundary as a Center Boundary. For the systems with three zones, we consider continuous piecewise linear systems where the central one is degenerate, that is, the determinant of its linear part vanishes. By moving one special parameter, we detect some new bifurcations exhibiting jump transitions both in the equilibrium location and in the appearance of limit cycles. In particular, we introduce the Scabbard Bifurcation, characterized by the birth of a limit cycle from a continuum of equilibrium points. / CAPES/DS: 33004153071P0 / CAPES/PDSE: 7038/2014-03

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.

Orientadores: Jose Manoel Balthazar, João Mauricio Rosario / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-08-05T10:03:06Z (GMT). No. of bitstreams: 1 Cassiano_Jeferson_D.pdf: 8294948 bytes, checksum: b7318ea3e310db82a9fd5af926a9cb2a (MD5) Previous issue date: 2005 / Resumo: Este trabalho tem como objetivo a determinação analítica da ocorrência de um tipo de caos (irregularidade) determinístico denominado Caos Homoclínico em algumas aplicações da Ciência da Engenharia como, por exemplo, a Robótica e a Teoria de Controle (Controle de Bifurcações e Caótico). Para isto, faz-se uso da chamada Teoria de Poincaré - Mel¿nikov que fornece uma forma analítica para a determinação do tipo de comportamento do sistema (regular ou irregular) / Abstract: This work make the analytical determination of the occurrence of a type of deterministic chaos (irregularity) called Homoclinic Chaos in some applications of the Science of Engineering and mechanics as, for example, the Robotics and the Theory of Control (Chaotic Control of Bifurcations so on). For that purpose, the Theory of Poincaré - Mel¿nikov is used that supplies an analytical form for the determination of the type of the system behavior of the system (regular or irregular) / Doutorado / Mecanica dos Sólidos e Projeto Mecanico / Doutor em Engenharia Mecânica

Le fonctionnement d'un neurone, unité fondamentale du système nerveux, intéresse de nombreuses disciplines scientifiques. Il existe ainsi des modèles mathématiques qui décrivent leur comportement par des systèmes d'EDO ou d'EDP. Plusieurs de ces modèles peuvent ensuite être couplés afin de pouvoir étudier le comportement de réseaux, systèmes complexes au sein desquels émergent des propriétés. Ce travail présente, dans un premier temps, les principaux mécanismes régissant ce fonctionnement pour en comprendre la modélisation. Plusieurs modèles sont alors présentés, jusqu'à celui de FitzHugh-Nagumo (FHN), qui présente une dynamique très intéressante.C'est sur l'étude théorique mais également numérique de la dynamique asymptotique et transitoire du modèle de FHN en EDO, que se concentre la seconde partie de cette thèse. A partir de cette étude, des réseaux d'interactions d'EDO sont construits en couplant les systèmes dynamiques précédemment étudiés. L'étude du phénomène de synchronisation identique au sein de ces réseaux montre l'existence de propriétés émergentes pouvant être caractérisées par exemple par des lois de puissance. Dans une troisième partie, on se concentre sur l'étude du système de FHN dans sa version EDP. Comme la partie précédente, des réseaux d'interactions d'EDP sont étudiés. On entreprend dans cette partie une étude théorique et numérique. Dans la partie théorique, on montre l'existence de l'attracteur global dans l'espace L2(Ω)nd et on donne des conditions suffisantes de synchronisation. Dans la partie numérique, on illustre le phénomène de synchronisation ainsi que l'émergence de lois générales telles que les lois puissances ou encore la formation de patterns, et on étudie l'effet de l'ajout de la dimension spatiale sur la synchronisation. / The neuron, a fundamental unit in the nervous system, is a point of interest in many scientific disciplines. Thus, there are some mathematical models that describe their behavior by ODE or PDE systems. Many of these models can then be coupled in order to study the behavior of networks, complex systems in which the properties emerge. Firstly, this work presents the main mechanisms governing the neuron behaviour in order to understand the different models. Several models are then presented, including the FitzHugh-Nagumo one, which has a interesting dynamic. The theoretical and numerical study of the asymptotic and transitory dynamics of the aforementioned model is then proposed in the second part of this thesis. From this study, the interaction networks of ODE are built by coupling previously dynamic systems. The study of identical synchronization phenomenon in these networks shows the existence of emergent properties that can be characterized by power laws. In the third part, we focus on the study of the PDE system of FHN. As the previous part, the interaction networks of PDE are studied. We have in this section a theoretical and numerical study. In the theoretical part, we show the existence of the global attractor on the space L2(Ω)nd and give the sufficient conditions for identical synchronization. In the numerical part, we illustrate the synchronization phenomenon, also the general laws of emergence such as the power laws or the patterns formation. The diffusion effect on the synchronization is studied.

Ce travail porte sur de nouvelles explosions de cycles (orbites périodiques), l'étude de leur structure par l'analyse qualitative, leur mise en évidence par simulation numérique (Auto, Xpp) et la discussion de leur pertinence dans des modèles mathématiques dans les neurosciences. De telles explosions se produisent dans les systèmes dynamiques lents-rapides. La plupart des neurones sont excitables, dès 1940, Hodgkin identifia trois classes fondamentales d'axones excitables distinguées par leurs réponses à un courant injecté d'amplitude variable. A l'aide de la fonction de Lambert, nous étudions la transition entre les types I et II par des explosions de cycle incomplètes, initiées par une bifurcation de Hopf singulière et qui se terminent dans une bifurcation homocline dans des systèmes une variable rapide/une variable lente. Vient ensuite une étude poussée du système de Hindmarsh-Rose. Il s'agit d'un système deux variables rapides/une variable lente qui produit des oscillations en salves (ou bursting). Nous généralisons la notion d'ensembles candidats-limites-périodiques (clp) aux systèmes tridimensionnels, il s'agit des ensembles invariants du système à la limite singulière. A l'aide de ces derniers, nous obtenons une description très fine de la déformation du cycle limite jusqu'à l'addition d'un nouveau spike au burst. Nous finissons par une étude de la minimalité du modèle de F. Clément et J.-P. Françoise. Ce dernier est un système 4D qui modélise l¿activité des neurones à GnRH. Nous étudions un système une variable rapide/deux variables lentes qui reproduit certaines des caractéristiques du modèle 4D, notamment des Mixed-Modes oscillations. / This thesis is focussed on the analysis of novel explosions of limit cycles (periodic orbits). We provide a study of their structure by qualitative analysis, exhibit evidences of their existence by numerical simulations (Auto, Xpp) and propose a discussion of their relevance in mathematical modeling for neurosciences. Such explosions occur in the slow-fast dynamical systems. Most of neurons are excitable, Hodgkin (1940) identified three fundamental classes of excitable axon distinguished by their responses to a current of variable amplitude injected. Using the Lambert function, we study the transition between types I and II by incomplete explosion of cycle. This explosion, produced by a planar vector field with one fast/one slow variable, is initiated by a singular Hopf bifurcation and ends via a homoclinic bifurcation. The next chapter proposed a study of the Hindmarsh-Rose system. This system, composed of one fast/ two slow variables, is well known to produce square wave bursting oscillation. We generalize the notion of candidate-limit-perodic sets (CLP-sets) to three-dimensional systems. A CLP-set is an invariant set of the system in the singular limit. Using these, we get a very acurate description of the limit cycle deformation under the variation of a parameter until the addition of a new spike to burst. Finally, we propose a study fot the minimality of the model introduced by F. Clement and J.-P. Françoise. The latter is a 4D system that models the activity of GnRH neurons. We study a system composed by one fast /two slow variables that reproduces some of the features of the 4D model, including Mixed-Modes oscillations.

We study the geometric and topological properties of strange non-chaotic attractors created in non-smooth saddle-node bifurcations of quasiperiodically forced interval maps. By interpreting the attractors as limit objects of the iterates of a continuous curve and controlling the geometry of the latter, we determine their Hausdorff and box-counting dimension and show that these take distinct values. Moreover, the same approach allows us to describe the topological structure of the attractors and to prove their minimality.

This master thesis deals with detection of blood-vessel bifurcations in retinal images and its properties. There are explained procedure of taking photographs of retina by fundus camera, optical coherence tomography (OCT) and scanning laser opthalmoscope (SLO) and properties of fundus images are described. In this thesis are mentioned some effective thresholding methods and there are explained the most important morphological operations with binary images, as well as with grayscale images. Detected bifurcations are used for image registration with second-order polynomial transformation using corresponding bifurcations.

Membrane structures are commonly used in many elds. The studies of thesestructures are of increasing interest. The two projects focus on the evaluations ofequilibrium states for uid-pressurized membranes under dierent loading conditions,and the corresponding instability behavior.The rst part of the current work discusses the instability behavior of a thin,planar, circular and initially horizontal membrane subjected to downwards or upwards uid pressure. The membrane structures exhibit large deformations under uid pressure. Various instability behaviors have been observed for dierent loadingparameters. Limit and bifurcation points have been detected for dierent loadingconditions. Dierent loading parameters have been used to interpret the instabilitybehavior. The eects on instability of parameters, the initial states of the membrane,and the chosen mesh have been discussed.The second part of the current work discusses instability behavior of a thin,spherical and closed membrane containing gas and uid placed on a horizontal rigidand non-friction plane. A multi-parametric loading has been described. By addingthe practically relevant controlling equations, the complex equilibrium paths werefollowed using the generalized path following algorithm, and the stability conclusionswere made dierently, according to the considered load parameters and theconstraints. A generalized eigenvalue analysis was used to evaluate the stabilitybehavior including the constraint eects. Fold line evaluations were performed toanalyze the parametric dependence of the instability behavior. A solution surfaceapproach was used to visualize the mechanical response under this multi-parametricsetting. / <p>QC 20151029</p>

L'un des enjeux majeurs actuellement en neurosciences est l'élaboration de modèles computationnels capables de reproduire les données obtenues expérimentalement par des méthodes d'imagerie et permettant l'étude de la relation structure-fonction dans le cerveau. Les travaux de modélisation dans cette thèse se situent à deux échelles et l'analyse des modèles a nécessité le développement d'outils théoriques et numériques dédiés. À l'échelle locale, nous avons proposé un nouveau modèle d'équations différentielles ordinaires générant des activités neuronales, caractérisé et classifié l'ensemble des comportements générés, comparé les sorties du modèle avec des données expérimentales et identifié les structures dynamiques sous-tendant la génération de comportements pathologiques. Ce modèle a ensuite été couplé bilatéralement à un nouveau compartiment modélisant les dynamiques de neuromédiateurs et leurs rétroactions sur l'activité neuronale. La caractérisation théorique de l'impact de ces rétroactions sur l'excitabilité a été obtenue en formalisant l'étude des variations d'une valeur de bifurcation en un problème d'optimisation sous contrainte. Nous avons enfin proposé un modèle de réseau, pour lequel la dynamique des noeuds est fondée sur le modèle local, incorporant deux couplages: neuronal et astrocytaire. Nous avons observé la propagation d'informations différentiellement selon ces deux couplages et leurs influences cumulées, révélé les différences qualitatives des profils d'activité neuronale et gliale de chaque noeud, et interprété les transitions entre comportements au cours du temps grâce aux structures dynamiques identifiées dans les modèles locaux. / A current issue in neuroscience is to elaborate computational models that are able to reproduce experimental data recorded with various imaging methods, and allowing us to study the relationship between structure and function in the human brain. The modeling objectives of this work are two scales and the model analysis need the development of specific theoretical and numerical tools. At the local scale, we propose a new ordinary differential equations model generating neuronal activities. We characterize and classify the behaviors the model can generate, we compare the model outputs to experimental data and we identify the dynamical structures of the neural compartment underlying the generation of pathological patterns. We then extend this approach to a new neuro-glial mass model: a bilateral coupling between the neural compartment and a new one modeling the impact of astrocytes on neurotransmitter concentrations and the feedback of these concentrations on neural activity is developed. We obtain a theoretical characterization of these feedbacks impact on neuronal excitability by formalizing the variation of a bifurcation value as a problem of optimization under constraint. Finally, we propose a network model, which node dynamics are based on the local neuro-glial mass model, embedding a neuronal coupling and a glial one. We numerically observe the differential propagations of information according to each of these coupling types and their cumulated impact, we highlight qualitatively distinct patterns of neural and glial activities of each node, and link the transitions between behaviors with the dynamical structures identified in the local models.