Neste trabalho foi realizado um mapeamento de ferramentas analíticas para representação e tratamento computacional de Sistemas Fuzzy. Este mapeamento evidenciou a existência de relações e a adequação do uso da Teoria Fuzzy na construção de modelos para a solução de problemas envolvendo Sistemas Dinâmicos e, em particular, de Sistemas Dinâmicos Caóticos. Propôs-se uma diferenciação entre dois tipos de Sistemas Dinâmicos Fuzzy (SDF\'s) - os Sistemas Dinâmicos Fuzzy Intrínsecos (SDFI\'s) e os Sistemas Dinâmicos Fuzzy Extrínsecos (SDFE\'s). Foram utilizados SDFE\'s na modelagem Fuzzy para a solução de problemas de fixação de trajetórias em sistemas caóticos. Foram desenvolvidos Estudos de Caso que permitiram verificar, por meio de simulações em bilhares e testes em circuito de Chua (este último implementado em protótipo físico) a adequação do uso desta técnica na solução destes problemas. No desenvolvimento da Tese foram obtidas as seguintes realizações relacionadas ao circuito de Chua (CCH): Tratamento computacional sobre circuito real; Utilização de um conversor analógico-digital de oito bits seguido por filtro passa-baixas para compensar a baixa resolução na leitura dos sinais; Utilização de circuito girador para implementar o indutor do CCH; Proposta e realização de um circuito inédito para definir o resistor de controle, via porta paralela do PC, de modo simples e de fácil reprodução. Com relação aos bilhares foram obtidas as seguintes realizações: Definição de um novo tipo de bilhar (Bilhar Newtoniano de Garms & Andrade); Desenvolvimento da análise detalhada das equações de simulação dos bilhares empregados nos Estudos de Caso. Ao rediscutir-se a Lógica Seqüencial Fuzzy definiu-se e desenvolveu-se, por meio da aplicação de realimentação em Circuitos Seqüenciais Fuzzy nos Sistemas Dinâmicos, um Astável Fuzzy (oscilações não-periódicas), o qual exemplifica um SDFI. Finalmente realizaram-se algumas interpretações da Física pela Teoria Fuzzy, utilizando-se o conceito de SDFI\'s. / A mapping of analytical tools for representation and computational treatment of Fuzzy Systems was made in this thesis. This mapping evidenced the existence of relations and the adequacy of the use of the Fuzzy Theory in the models construction for the problems solution involving dynamic systems e, in particular, of chaotic systems. A differentiation was considered about two types of Fuzzy Dynamic Systems - the Intrinsic Fuzzy Dynamic Systems (IFDS) and the Extrinsic Fuzzy Dynamic Systems (EFDS). The EFDS in the Fuzzy modeling is used for the problems solution of trajectories setting in chaotic systems. Case Studies had been developed that allow to verify, by means of simulation in billiards and tests in circuit of Chua (implemented in physical prototype), the adequacy of the use of this strategy in the solution of these problems. Related with Chua circuit, can be mentioned the following achievements: Computational treatment on real circuit; Use of a 8-bits AD converter followed by lowpass filter to compensate this low resolution signals reading; Use of gyrator circuit to implement the inductor used in this circuit; Proposal and accomplishment of a circuit to define the control resistor, via PC parallel port, of simple reproduction. Related with billiards, the following achievements are mentioned: Definition of a new billiard - Garms & Andrade Newtonian Billiard; Development of detailed equations of the simulations billiards analysis. When discussing again the Sequential Logic Fuzzy, is defined and developed, by means of the application of feedback in Sequential Circuits Fuzzy in the Dynamic Systems, an Astable Fuzzy (non-periodic oscillations), which exemplifies an IFDS. Finally, some interpretations of the Physics for the Fuzzy Theory are also presented with the use of the IFDS concept.

Nas últimas décadas, vários sistemas de comunicação baseados em sincronismo caótico têm sido propostos na literatura como alternativa a sistemas de espalhamento espectral que melhoram o nível de privacidade na transmissão da mensagem. No entanto, devido à falta de robustez do sincronismo caótico, um pequeno nível de ruído ou uma simples imperfeição no canal é suficiente para impedir a comunicação. Neste trabalho, equalizadores adaptativos são utilizados para permitir a comunicação em um sistema de comunicação baseado em caos quando a resposta em frequência do canal não é ideal. São propostos algoritmos de equalização baseados em versões modificadas do algoritmo normalized least-mean-squares para a versão de tempo discreto do sistema de comunicação baseado no modelo de sincronismo de Wu e Chua. Para esses algoritmos, é calculado o intervalo para a escolha do passo de adaptação para evitar a divergência. Como geradores de sinais caóticos (GSC), são utilizados os mapas de Hénon e de Ikeda e, para a codificação da mensagem, são consideradas duas funções, sendo uma baseada na multiplicação da mensagem por um dos estados do GSC e a outra baseada na soma da mensagem com um dos estados do GSC. Os resultados de simulação indicam que os algoritmos propostos são capazes de equalizar o canal de comunicação e permitir o sincronismo caótico em diferente cenários. / In the last decades, many communication systems applying synchronism of chaotic systems have been proposed as an alternative spread spectrum modulation that improves the level of privacy in data transmission. However, due to the lack of robustness of chaos synchronization, even a low level of noise or minor channel imperfections are enough to hinder communication. In this work, adaptive equalizers are used to enable chaotic synchronization when the communication channel is not ideal. Adaptive equalization algorithms are proposed based on a modified version of the normalized least-mean-squares algorithm, considering the discrete-time version of the communication system based on Wu and Chuas synchronization model. For these algorithms, the interval for the choice of the step-size is computed, in order to avoid divergence. The Hénon and the Ikeda maps are used as chaotic signal generators (CSG) and two functions are considered to encode the message, one based on the multiplication of the message by one of the states of the CSG and the other based on the addition of the message to one of the states of the CSG. Simulation results show that the proposed algorithms can successfully equalize the channel in different scenarios.

Alguns métodos aproximados são sugeridos na literatura relacionada para encontrar a resposta de sistemas com amortecimento não-proporcional. Muitas vezes procura-se estabelecer um critério para aproximar o amortecimento não-proporcional por um modelo de amortecimento proporcional. Neste trabalho foram utilizadas simulações de modelos dinâmicos com três graus de liberdade, com amortecimento não proporcional, a fim de analisar os valores obtidos para as freqüências naturais, estimados a partir dos autovalores resultantes desses modelos. Os cálculos das freqüências naturais e dos amortecimentos modais foram feitos admitindo-se a validade das relações entre estes parâmetros e os autovalores do problema como são bem conhecidas no caso do amortecimento proporcional. Observa-se que, para o caso de amortecimento não-proporcional, este procedimento pode levar a erros significativos na avaliação destes parâmetros. Nos problemas simulados é possível quantificar os erros nas avaliações das freqüências naturais, sendo significativos para fatores de amortecimentos altos. Observa-se que para os fatores de amortecimento não é possível quantificar estes erros, sendo que seus valores são apenas aproximações baseadas na teoria de amortecimento proporcional. Este trabalho apresenta dados que possibilitam uma discussão sobre as diferenças encontradas entre os valores das freqüências naturais e os valores estimados pelas expressões clássicas do amortecimento proporcional. / Some approximate methods are suggested in the related literature to find the output of mechanical systems with non-proportional damping. Often they try to establish a criterion that approximates the non-proportional damping to proportional damping model. In this work, stimulations of dynamics models of three degree of freedom with non-proportional damping were used to examine the values of natural frequencies, estimated from the eigenvalues obtained by these models. The calculations of natural frequencies and modal damping ratio were performed assuming the validity of the relationship between these parameters and the well known eigenvalues of the problem in the proportional damping case. In the simulated problems is possible to quantify the errors in the evaluations of the natural frequencies and this errors are significant for the case where the damping factors are high. It is observed that for the damping factors it is not possible to quantify these errors, and their magnitudes are only approximations based on the theory of proportional damping. This work presents data which enables a discussion about the differences between the magnitude of natural frequencies and the magnitude estimated by the classic equations of proportional damping.

This naturalistic exploratory multiple case study of the academic writing activity of L2 writers enrolled in an introductory Spanish literature course reveals the complex dynamicity of intertextual activity and L2 development. The writing tasks, designed for communicative practice rather than for mastery of a genre, required students to upload Microsoft Word documents to the learning management software’s dropbox, thus necessitating their engagement with multiple digitally mediated resources. Participants completed the assignment outside of class in a computer lab, where data were collected, including observational field notes, screen recordings, and stimulated recall, and semi-structured interviews about the participants’ use and perception of digital resources. Findings show that these students employed many strategies with a variety of resources, including online dictionaries, translators, and original and translated texts, when experiencing a lexical gap while writing. A close examination of second language writers’ intertextual engagement with the affordances provided by these digitally mediated resources through an analytical frame informed by dynamic systems theory (Larsen-Freeman & Cameron, 2008a) reveals idiosyncratic use and evidence of emergent word and strategy learning. Pedagogical implications, including the need to start where students are, are discussed.

The control theory of nonlinear systems has been receiving increasing attention in recent years, both for its technical importance as well as for its impact in various fields of application. In several key areas, such as aerospace, chemical and petrochemical industries, bioengineering, and robotics, a new practical application for this tool appears every day. System nonlinearity is characterized when at least one component or subsystem is nonlinear. Classical methods used in the study of linear systems, particularly superposition, are not usually applied to the nonlinear systems. It is necessary to use other methods to study the control of these systems. For a wide class of nonlinear systems, a rather important structural feature comes from the strong nonlinearity appearing as coupling between spectrally decoupled parts of the system. Even in the case of low frequencies, where lumped models can still be employed the nonlinear coupling between parts of the system requires specific treatment, using advanced mathematical tools. In this context, an alternative, frequency domain approach is pursued here. In the rest of this work, a specific system form of linearly decoupled but nonlinearly coupled subsystems is examined. The mathematical toolbox of the Hilbert transform is appropriately introduced for obtaining two low-pass subsystems that form an equivalent description of the essential overall system dynamics. The nonlinear coupled dynamics is investigated systematically by partitioning the coupled system state vector in such a way as to fully exploit the low-pass and the band-pass intrinsic features of free dynamics. In particular, by employing the Hilbert Transform, a low-pass equivalent system is derived. Then, a typical case is investigated thoroughly by means of numerical simulation of the original coupled low and band-pass, real-state-variable system and the low-pass-equivalent, complex-state-variable derived one. The nonlinear model equations considered here pave the way for a systematic investigation of nonlinear feedback control options designed to operate mechatronic transducers in energy harvesting, sensing or actuation modes.

This study applied a contemporary dynamic systems methodology (state space grids) to examine how the structure of parent-child coping interactions, above and beyond the content of such interactions, influences adjustment (i.e., internalizing problems, externalizing problems, and coping efficacy) over time in middle childhood. A community sample of children (N = 65) completed a stressful laboratory task with a parent present, during which parent and child behavior were observed. Parent behavior during the task was coded using a socialization of coping framework. Parents' verbal suggestions to their child about how to cope with the stressful task were coded as primary control engagement suggestions (i.e., suggestions encouraging the child to directly address and attempt to change the stressor or the child's associated emotions), secondary control engagement suggestions (i.e., suggestions encouraging the child to change their own reaction to their stressor), or disengagement suggestions (i.e., suggestions encouraging the child to take their attention away from the stressor). Child coping verbalizations and behavior during the task was coded as either engaging with the stressor or disengaging from the stressor. The structure of the parent-child coping interaction was measured in two ways: (a) dyadic flexibility, defined as the dispersion of parent and child behavior across all possible behaviors and the number of transitions between different parent or child behaviors during the task, and (b) attractor (i.e., parent-focused, child-focused, or dyad-focused interaction pattern) strength, defined as the number of visits, duration per visit, and return time to that interaction pattern. Child adjustment outcomes were measured using parent-report (internalizing and externalizing problems) and child-report (coping efficacy) at baseline and a 6-month follow-up. Linear regression analyses were conducted examining dyadic flexibility and the proposed attractors as predictors of child adjustment, while accounting for demographic variables, attractor content, and adjustment at baseline. Findings suggested that dyadic flexibility in the parent-child coping interaction was largely adaptive for child adjustment, whereas attractor strength demonstrated a more complex relationship with child adjustment outcomes. This study demonstrates the utility of applying state-space grids to examine the structure of parent-child coping interactions, in addition to content, as predictors of child adjustment. Furthermore, this study offers novel, detailed information about coping interactions in families with children in middle childhood. Clinical implications, limitations, and future directions are discussed.

Inflammation in the lungs can occur for many reasons, from bacterial infections to stretch by mechanical ventilation. In this work we compare and contrast various mathematical models for lung injuries in the categories of acute infection, latent versus active infection, and particulate inhalation. We focus on systems of ordinary differential equations (ODEs), agent-based models (ABMs), and Boolean networks. Each type of model provides different insight into the immune response to damage in the lungs. This knowledge includes a better understanding of the complex dynamics of immune cells, proteins, and cytokines, recommendations for treatment with antibiotics, and a foundation for more well-informed experiments and clinical trials. In each chapter, we provide an in-depth analysis of one model and summaries of several others. In this way we gain a better understanding of the important aspects of modeling the immune response to lung injury and identify possible points for future research.

Delay differential equations have a wide range of applications in engineering. This work is devoted to the analysis of delay Duffing equation, which plays a crucial role in modeling performance on demand Micro Electro Mechanical Systems (MEMS). We start with the stability analysis of a linear delay model. We also show that in certain cases the delay model can be efficiently approximated with a much simpler model without delay. We proceed with the analysis of a non-linear Duffing equation. This model is a significantly more complex mathematical model. For instance, the existence of a periodic solution for this equation is a highly nontrivial question, which was established by Struwe. The main result of this work is to establish the existence of a periodic solution to delay Duffing equation. The paper claimed to establish the existence of such solutions, however their argument is wrong. In this work we establish the existence of a periodic solution under the assumption that the delay is sufficiently small.

Intelligent agents are designed to interact with, and learn about, their environment so that they can act purposefully towards a goal. One class of problems encountered in building such agents is learning how to respond to dynamic systems with a continuous state space. The goals of this dissertation are to develop a framework for understanding the behaviour of partitioned dynamic systems with continuous underlying state and to translate this framework into algorithms which adaptively form a partition of the continuous space such that the partitioned system is more easily learned and controlled, and such that the control law may be easily explained in intuitive ways. Currently, algorithms which learn a control policy for partitioned continuous state space systems treat the partitioned system as an approximation to a Markov chain. I give conditions for the partitioned system to be a Markov chain, a semi-Markov process and a new class of system, a weak-semi-Markov process. The weak-semi-Markov model is shown to model partitioned dynamic systems with greater economy than other surveyed models. The behaviour of a partitioned state space system in the area around the region boundaries is also considered. I use the theory of sliding surfaces, and some heuristic arguments to recommend region boundary shape and position. The concept of 'staying on the boundary' then becomes a robust and relatively easy subgoal within the control algorithm. The concept of 'reaching the sliding surface' as a subgoal is used as the basis for an intuitive explanation of the learnt controller. I present an algorithm based on this concept which explains the behaviour of a learnt controller in ways not previously available to a machine learning algorithms. Finally, the Markov Property and the theory of Sliding Mode Control are used as the basis of a class of recursive algorithms. These algorithms adaptively find a partition, and simultaneously use this partition in conjunction with one of five reinforcement learning algorithms to find a control policy based on that partition. This technique is shown to work very well in learning, controlling and explaining a variety of physical systems, from a monorail to a container crane.

The design process includes many different activities inwhich various computational mechanics tools are used forbehaviour modelling of mechanical systems and their buildingblocks, e.g. machine elements. These tools usually supportlarge and complex models and they produce large quantities ofdata with a high degree of complexity. In these situations,efficient data management and the ability to search and sharedata are important issues to achieve an efficient designprocess. Today, this ability is usually not supported by theindividual applications even though this probably would improveand facilitate the ability to search for data on a higher levelin the engineering information system. This work investigates the ability of searching andcomparing analysis data within behaviour models of technicalsystems as well as over the analysis results. This is done byinvestigating the potential benefits of integrating moderndatabase technology with a multibody system (MBS) analysissoftware in the same manner that has been successfully done forbusiness and administrative applications. This has resulted inan implemented pilot system, named MECHAMOS, that integratesthe main-memory resident object-relational database managementsystem (DBMS) AMOSwith the symbolic multibody system (MBS)software SOPHIA operating in MapleV. This provides MECHAMOSwith both symbolic and numeric mathematical capabilities forMBS analysis and data management capabilities to search andcompare engineering data in the database. The approach, making data managing tools available in acomputer aided engineering software, considerably improves theanalysis of technical systems. The analysis is brought to ahigher level through the available query language and thedesired data is specified, fairly intuitively, in a query. Whenthe query is processed, the DBMS knows how to retrieve andautomatically derive the required data. As shown in someexamples, the ability to search over stored and derived data inthe database is not restricted to a single MBS-model inMECHAMOS. Because of the implemented materialisation handling,it is also possible to search, combine, and compare data fromseveral simulation results which are based on several differentmodels in the database. This extends the ability to performoptimisation from a traditional parameter study to thepossibility to analyse and compare different technical conceptsthrough the query language and hereby retrieve those conceptsthat fulfil certain requirements. If submodel techniques aresupported, queries over a set of components in the databasewould automatically create, analyse and compare the possibleconcepts. This would assist the designer in choosing the bestcomponents for a design.