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Many chaotic and complicated systems cannot be analysed by traditional methods. In 1987 P.Bak, C.Tang, and K.A.Wiesenfeld developed a new concept called Self-Organised Criticality (SOC) to explain the behaviour of composite systems containing a large number of elements that interact over a short range. In general this theory applies to complex systems that naturally evolve to a critical state in which a minor event starts a chain reaction that can affect any number of elements in the system. It was later shown that many complex phenomena such as flux pinning in superconductors, dynamics of granular systems, earthquakes, droplet formation and biological evolution show signs of SOC. The dynamics of complex systems in nature often occurs in terms of punctuation, or avalanches rather than following a smooth, gradual path. Extremal dynamics is used to model the temporal evolution of many different complex systems. Specifically the Bak-Sneppen evolution model, the Sneppen interface depinning model, the Zaitsev flux creep model, invasion percolation, and several other depinning models. This thesis considers extremal dynamics at constant flux where M>1 smallest barriers are simultaneously updated as opposed to models in the limit of zero flux where only the smallest barrier is updated. For concreteness, we study the Bak-Sneppen (BS) evolution model [Phys. Rev. Lett. 71, 4083 (1993)]. M=1 corresponds to the original BS model. The aim of the present work is to understand analytically through mean field theory the random neighbour version of the generalised BS model and verify the results against the computer simulations. This is done in order to scrutinise the trustworthiness of our numerical simulations. The computer simulations are found to be identical with results obtained from the analytical approach. Due to this agreement, we know that our simulations will produce reliable results for the nearest neighbour version of the generalised BS model. Since the nearest neighbour version of the generalised BS model cannot be solved analytically, we have to rely on simulations. We investigate the critical behaviour of both versions of the model using the scaling theory. We look at various distributions and their scaling properties, and also measure the critical exponents accurately verifying whether the scaling relations holds. The effect of increasing from M=1 to M>1 is surprising with dramatic decrease in size of the scaling regime.

Systems of globally coupled phase oscillators can have robust attractors that are heteroclinic networks. Such a heteroclinic network is generated, where the phases cluster into three groups, within a specific regime of parameters when the phase oscillators are globally coupled using the function $g(\varphi) = -\sin(\varphi + \alpha) + r \sin(2\varphi + \beta)$. The resulting network switches between 30 partially synchronised states for a system of $N=5$ oscillators. Considering the states that are visited and the time spent at those states a spatio-temporal code can be generated for a given navigation around the network. We explore this phenomenon further by investigating the effect that noise has on the system, how this system can be used to generate a spatio-temporal code derived from specific inputs and how observation of a spatio-temporal code can be used to determine the inputs that were presented to the system to generate a given coding. We show that it is possible to find chaotic attractors for certain parameters and that it is possible to detail a genetic algorithm that can find the parameters required to generate a specific spatio-temporal code, even in the presence of noise. In closing we briefly explore the dynamics where $N>5$ and discuss this work in relation to winnerless competition.

abstract: In this thesis I introduce a new direction to computing using nonlinear chaotic dynamics. The main idea is rich dynamics of a chaotic system enables us to (1) build better computers that have a flexible instruction set, and (2) carry out computation that conventional computers are not good at it. Here I start from the theory, explaining how one can build a computing logic block using a chaotic system, and then I introduce a new theoretical analysis for chaos computing. Specifically, I demonstrate how unstable periodic orbits and a model based on them explains and predicts how and how well a chaotic system can do computation. Furthermore, since unstable periodic orbits and their stability measures in terms of eigenvalues are extractable from experimental times series, I develop a time series technique for modeling and predicting chaos computing from a given time series of a chaotic system. After building a theoretical framework for chaos computing I proceed to architecture of these chaos-computing blocks to build a sophisticated computing system out of them. I describe how one can arrange and organize these chaos-based blocks to build a computer. I propose a brand new computer architecture using chaos computing, which shifts the limits of conventional computers by introducing flexible instruction set. Our new chaos based computer has a flexible instruction set, meaning that the user can load its desired instruction set to the computer to reconfigure the computer to be an implementation for the desired instruction set. Apart from direct application of chaos theory in generic computation, the application of chaos theory to speech processing is explained and a novel application for chaos theory in speech coding and synthesizing is introduced. More specifically it is demonstrated how a chaotic system can model the natural turbulent flow of the air in the human speech production system and how chaotic orbits can be used to excite a vocal tract model. Also as another approach to build computing system based on nonlinear system, the idea of Logical Stochastic Resonance is studied and adapted to an autoregulatory gene network in the bacteriophage λ. / Dissertation/Thesis / Ph.D. Electrical Engineering 2011

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This work is concerned with the study of flow stability and turbulence control - two old but still open problems of fluid mechanics. The topics are distinct and are (currently) approached from different directions and with different strategies. This thesis reflects this diversity in subject with a difference in geometry and, consequently, flow structure: the first problem is approached in the study of the flow in a toroidal pipe, the second one in an attempt to reduce the drag in a turbulent channel flow. The flow in a toroidal pipe is chosen as it represents the common asymptotic limit between spatially developing and helical pipes. Furthermore, the torus represents the smallest departure from the canonical straight pipe flow, at least for small curvatures. The interest in this geometry is twofold: it allows us to isolate the effect of the curvature on the flow and to approach straight as well as helical pipes. The analysis features a characterisation of the steady solution as a function of curvature and the Reynolds number. The problem of forcing fluid in the pipe is addressed, and the so-called Dean number is shown to be of little use, except for infinitesimally low curvatures. It is found that the flow is modally unstable and undergoes a Hopf bifurcation that leads to a limit cycle. The bifurcation and the corresponding eigenmodes are studied in detail, providing a complete picture of the instability. The second part of the thesis approaches fluid mechanics from a different perspective: the Reynolds number is too high for a deterministic description and the flow is analysed with statistical tools. The objective is to reduce the friction exerted by a turbulent flow on the walls of a channel, and the idea is to employ a control strategy independent of the small, and Reynolds number-dependent, turbulent scales. The method of choice was proposed by Schoppa &amp; Hussain [Phys. Fluids 10:1049-1051 (1998)] and consists in the imposition of streamwise invariant, large-scale vortices. The vortices are re-implemented as a volume force, validated and analysed. Results show that the original method only gave rise to transient drag reduction while the forcing version is capable of sustained drag reduction of up to 18%. An analysis of the method, though, reveals that its effectiveness decreases rapidly as the Reynolds number is increased. / <p>QC 20161004</p>

Made available in DSpace on 2017-07-10T17:11:52Z (GMT). No. of bitstreams: 1 Texto completo - Rosiney.pdf: 7631119 bytes, checksum: 43c0461bb49060121b74d945a88d53d4 (MD5) Previous issue date: 2012-11-26 / The present work proposes a study of the dynamics of a gyroscope using simulated data of an analytical model by comparing with experimental data. Classical mechanical modeling approaches are used to identify the equilibrium points, stability and verification of the regions where the motion equations of the gyroscope can present regular or chaotic behavior. The Lyapunov exponents are identified through the standard method, Eckmann-Ruelle Method, Wolf method with time series and the 0-1 test. The results achieved illustrate the main advantages and drawbacks of each method and allow to observe qualitatively and quantitatively information about the motion of the gyroscope used. / Este trabalho propõe um estudo da dinâmica de um giroscópio usando dados de simulação de um modelo analítico comparando com dados experimentais. Verifica-se a modelagem usando mecânica clássica, estudo de pontos de equilíbrio, estabilidade e verificação de regiões onde o movimento do giroscópio pode ficar regular ou caótico. Os expoentes de Lyapunov são identificados usando o método padrão, método de Eckmann-Ruelle, método deWolf com séries temporais e o teste 0-1. Os resultados alcançados nesta dissertação permitiram comparar as principais vantagens e desvantagens de cada um dos métodos e extrair informações qualitativas e quantitativas sobre o movimento do giroscópio em estudo.

Orientador: Masayoshi Tsuchida / Banca: José Manoel Balthazar / Banca: Cláudio Agnaldo Buzzi / Resumo: Este trabalho apresenta um estudo de um pêndulo eletromecânico com excitação vertical utilizando a teoria de perturbações. O objetivo é fazer um estudo analítico para verificar os efeitos de ressonância no estado estacionário do sistema, efeitos esses provocados por alguns valores de freqüência do sistema dinˆamico. As equações do sistema dinâmico estudado apresentam características que impedem a obtenção de soluções analíticas devido à presença de termos não lineares, e ainda exibem interações ressonantes entre bloco, motor e pêndulo. A análise feita considerou o sistema com ressonância entre o bloco e o motor, mas foi descartada a interação ressonante com o pêndulo. Como a excitação no suporte é vertical, em primeira aproximação a equação do pêndulo é a equação de Mathieu. Devido à presença de um termo não linear nesta equação, foi feito também um estudo com a teoria de perturbações para obter uma solução analítica aproximada, tomando como exemplo a equação de Mathieu analisada no estudo desenvolvido por Nayfeh. As equações para o estado estacionário do sistema foram obtidas através da aplicação de um método de perturbação. O estudo dessas equações foi baseado no trabalho desenvolvido por Kononenko, e os resultados obtidos são análogos, pois o sistema dinâmico deste estudo e o sistema dinâmico considerado por Kononenko guardam certa semelhança. / Abstract: In this work a study of an electromechanical pendulum with a vertical excitation is done using the Perturbation theory. The main objective is to make an approximate analytic study to verify the effects of resonance at the stationary state of the system, effects that are caused by some values of frequencies of the dynamic system. The equations of the system show characteristics that don't permit the analytic solutions because of presence of nonlinear terms and there are resonant interactions between the block, the eccentric mass and the pendulum. In this analysis the resonance between the block and the eccentric mass was considered, but the resonance with the pendulum was ignored. As the excitation of the support is vertical, the first approximation of the equation of the pendulum is a Mathieu equation. Due to the presence of one nonlinear term in this equation, a study with the perturbation theory was performed to get a solution at first approximation, following the study made by Nayfeh. The equations for the stationary state were taken through the application of one perturbation method. The study of these equations was based on the work developed by Kononenko and the results obtained are similar, because the dynamic system of this work and the system considered by Kononenko keep certain similarities. / Mestre

Resumen: En esta tesis doctoral se presentan tres modelos matemáticos que describen el comportamiento de dos enfermedades parasitarias con vector de transmisión; de los cuales dos modelos están dedicados a la Toxoplasmosis donde se explora la dinámica de la enfermedad a nivel de la población humana y de gatos domésticos. Los gatos juegan un papel de agentes infecciosos del Toxoplasma gondii. La dinámica cualitativa del modelo es determinada por el umbral básico de reproducción, R0. Si el parámetro R0 < 1, entonces la solución converge al punto de equilibrio libre de la enfermedad. Por otro lado, si R0 > 1, la convergencia es al punto de equilibrio endémico. Las simulaciones numéricas ilustran diferentes dinámicas en función del parámetro umbral R0 y muestra la importancia de este parámetro en el sector salud. Finalmente la Babesiosis bovina se modela a partir de cinco ecuaciones diferenciales ordinarias, que permiten explicar la influencia de los parámetros epidemiológicos en la evolución de la enfermedad. Los estados estacionarios del sistema y el número básico de reproducción R0 son determinados. La existencia del punto endémico y libre de enfermedad se expone, puntos que dependen del R0, ratificando la importancia del parámetro umbral en la salud publica. Objetivo: Construir modelos matemáticos epidemiológicos aplicados a enfermedades parasitarias (Toxoplasmosis y Babesiosis) con vector de transmisión. Metodología: Para la construcción de los modelos matemáticos epidemiológicos es necesario representar la enfermedad a partir de modelos de flujo, permitiendo ver la dinámica de la población entre los diferentes estadíos de la enfermedad, dichos movimientos son analizados a partir de sistemas dinámicos, análisis matemático y métodos numéricos; con estas herramientas es posible hacer un estudio detallado del modelo, permitiendo calcular parámetros umbrales que dominan la dinámica de la enfermedad y a su vez simular escenarios reales e hipotéticos. / Aranda Lozano, DF. (2011). Modeling of parasitic diseases with vector of transmission: toxoplasmosis and babesiosis bovine [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/11539 / Palancia

No / An adaptive iterative learning control approach is proposed for a class of single-input single-output uncertain nonlinear systems with completely unknown control gain. Unlike the ordinary iterative learning controls that require some preconditions on the learning gain to stabilize the dynamic systems, the adaptive iterative learning control achieves the convergence through a learning gain in a Nussbaum-type function for the unknown control gain estimation. This paper shows that all tracking errors along a desired trajectory in a finite time interval can converge into any given precision through repetitive tracking. Simulations are carried out to show the validity of the proposed control method.