Thesis (Ph.D.)--Ohio University, June, 2003. / Title from PDF t.p. Includes bibliographical references (leaves 205-239)

Thesis (Ph. D.)--University of Oregon, 2006. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 126-128). Also available for download via the World Wide Web; free to University of Oregon users.

Orientador: Gerson Francisco / Banca: Hilda Cerdeira / Banca: Fernando Fagundes Ferreira / Banca: Antonio Fernando Crepaldi / Banaca: Camilo Rodrigues Neto / Resumo: Este trabalho trata de dois temas principais: a reamostragem de séries temporais caóticas e a análise de redes de mapas acoplados. A reamostragem de séries temporais é estudada com o objetivo de encontrar uma incerteza para os invariantes medidos de um sistema dinâmico. Quando um invariante, tal como o expoente de Lyapunov, é obtido a partir de uma série temporal, freqüentemente este valor é calculado sem que seja associada uma medida de incerteza. Isto pode causar problemas, às vezes inviabilizando determinar se um sistema é realmente caótico. No processo de reamostragem outras séries temporais, que apresentam as mesmas propriedades dinâmicas da série original, são criadas. O processo de reamostragem é baseado nos métodos de previsão de uma série temporal. Depois que várias séries temporais são obtidas, cada uma delas é utilizada para medir um invariante do sistema, no caso o exponente de Lyapunov. Cada uma das séries apresenta um valor diferente para este expoente, assim obtém-se uma distribuição de valores para tal parâmetro. Com esta distribuição é possível calcular várias estatísticas, como o desvio padrão e alguns percentis para a distribuição. Nesta tese também é realizado um estudo sobre redes de mapas acoplados. Foram analisadas redes com dimensões: um, dois e três. Para cada um destes casos foram analisadas as propriedades estatísticas, assim como as propriedades dinâmicas. A partir destas análises, é mostrado que as séries temporais destes mapas apresentam auto-similaridade. Além disso, foi possível verificar que, com o aumento da dimensão, a série temporal torna-se mais correlacionada / Abstract: This work delas with two main themes: the resampling of time series and the analysis of coupled maps. The purpose of studying time series resampling is to find uncertainty intervals for the invariants of dynamical systems. When an invariant, such as the Lyapunov exponent, is obtained from the time series, it is frequently the case that no uncertainty interval is computed. This may cause problems, even making it unfeasible to determine if a system is really chaotic. In the resampling process several time series are created, that share the same dynamical properties of the original series. This resampling process is based on methods of prediction of a time series. After several time series are obtained, each one is used to measure an invariant of the system, in this case the Lyapunov exponent. Each series presents a distinct value for this exponent, and thus a distribution of values is obtained the parameter. With this distribution it is possible to calculate several statistics, such as the standard deviation and for the distribution. This thesis also examines a study about coupled maps. It was implemented grids with dimensions 1, 2 and 3. For each case the statistical, as well as dynamical properties were analyzed. From these analyses it is shown that the time series of these maps show self-similarity. In addition, it was possible to verify that, the series becomes more correlates as the dimension is increased / Doutor

The objective of this thesis is to propose fundamental concepts, analytical and numerical tools, and approaches to characterize, understand, and better observe complex systems. The scientific contribution of this thesis can be separated in tree topics. In the first one, we show how to theoretically estimate the Mutual Information Rate (MIR), the amount of mutual information transmitted per unit of time between two time-series. We then show how a quantity derived from it can be successfully used to infer the network structure of a complex system. The proposed inference methodology shows to be robust in the presence of additive noise, different time-series lengths, and heterogeneous node dynamics and coupling strengths. It also shows to be superior in performance for networks formed by nodes possessing different time-scales, as compared to inference methods based on mutual information (MI). In the second topic, a deep analysis of causality from the space-time properties of the observed probabilistic space is performed. We show the existence of special regions in the state space which indicate variable ranges responsible for most of the information exchanged between two variables. We define a new causality measure named CaMI that explores a property we have understood: in order to detect if there is a flow of information from X to Y, one only needs to check the positiveness of the MI between trajectories in X and Y, however assuming that the observational resolution in Y is larger than in X. Moreover, we show how the assessment of causality can be done when we consider partitions with arbitrary, but equal rectangular cells in the probabilist space, what naturally facilitates the calculation of CaMI. In the third topic, we develop a symbolic coefficient of observability that allows us to understand what is the reduced set of accessible variables to observe a complex system, such that it can be fully reconstructed from the set of observed variables, regardless of its dimension. Using this symbolic coefficient, we explain how it is possible to compare different complex systems from the point of view of observability and how to construct systems of any dimensionality that can be fully observed by only one variable.

Numerous examples arise in fields ranging from mechanics to biology where disappearance of Chaos can be detrimental. Preventing such transient nature of chaos has been proven to be quite challenging. The utility of Reinforcement Learning (RL), which is a specific class of machine learning techniques, in discovering effective control mechanisms in this regard is shown. The autonomous control algorithm is able to prevent the disappearance of chaos in the Lorenz system exhibiting meta-stable chaos, without requiring any a-priori knowledge about the underlying dynamics. The autonomous decisions taken by the RL algorithm are analyzed to understand how the system’s dynamics are impacted. Learning from this analysis, a simple control-law capable of restoring chaotic behavior is formulated. The reverse-engineering approach adopted in this work underlines the immense potential of the techniques used here to discover effective control strategies in complex dynamical systems. The autonomous nature of the learning algorithm makes it applicable to a diverse variety of non-linear systems, and highlights the potential of RLenabled control for regulating other transient-chaos like catastrophic events. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2020. / FAU Electronic Theses and Dissertations Collection

The design implications of chaos theory are explored. What does this theory mean, if anything, to landscape architecture or architecture? In order to investigate these questions, the research was divided into four components relevant to design. First, philosophical- chaos offers a nonlinear understanding about place and nature. Second, aesthetical-fractals describe a deep beauty and order in nature. Thirdly, modeling-it is a qualitative method of modeling natural processes. Lastly, managing- concepts of chaos theory can be exploited to mimic processes found in nature. These components draw from applications and selected literature of chaos theory. From these research components, design implications were organized and concluded. Philosophical implications, offer a different, nonlinear realization about nature for designers. Aesthetic conclusions, argue that fractal geometry can articulate an innate beauty (a scaling phenomenon) in nature. Modeling, discusses ways of using chaos theory to visualize the design process, a process which may be most resilient when it is nonlinear. The last research chapter, managing, applications of chaos theory are used to illustrate how complex form, like that in nature, can be created by designers. / Master of Landscape Architecture

No description available.

Thesis (MSc)-- Stellenbosch University, 2003. / ENGLISH ABSTRACT: This thesis implements and evaluates two prediction techniques used to forecast deterministic chaotic time series. For a large number of such techniques, the reconstruction of the phase space attractor associated with the time series is required. Embedding is presented as the means of reconstructing the attractor from limited data. Methods for obtaining the minimal embedding dimension and optimal time delay from the false neighbour heuristic and average mutual information method are discussed. The first prediction algorithm that is discussed is based on work by Sauer, which includes the implementation of the singular value decomposition on data obtained from the embedding of the time series being predicted. The second prediction algorithm is based on neural networks. A specific architecture, suited to the prediction of deterministic chaotic time series, namely the time dependent neural network architecture is discussed and implemented. Adaptations to the back propagation training algorithm for use with the time dependent neural networks are also presented. Both algorithms are evaluated by means of predictions made for the well-known Lorenz time series. Different embedding and algorithm-specific parameters are used to obtain predicted time series. Actual values corresponding to the predictions are obtained from Lorenz time series, which aid in evaluating the prediction accuracies. The predicted time series are evaluated in terms of two criteria, prediction accuracy and qualitative behavioural accuracy. Behavioural accuracy refers to the ability of the algorithm to simulate qualitative features of the time series being predicted. It is shown that for both algorithms the choice of the embedding dimension greater than the minimum embedding dimension, obtained from the false neighbour heuristic, produces greater prediction accuracy. For the neural network algorithm, values of the embedding dimension greater than the minimum embedding dimension satisfy the behavioural criterion adequately, as expected. Sauer's algorithm has the greatest behavioural accuracy for embedding dimensions smaller than the minimal embedding dimension. In terms of the time delay, it is shown that both algorithms have the greatest prediction accuracy for values of the time delay in a small interval around the optimal time delay. The neural network algorithm is shown to have the greatest behavioural accuracy for time delay close to the optimal time delay and Sauer's algorithm has the best behavioural accuracy for small values of the time delay. Matlab code is presented for both algorithms. / AFRIKAANSE OPSOMMING: In hierdie tesis word twee voorspellings-tegnieke geskik vir voorspelling van deterministiese chaotiese tydreekse ge"implementeer en geevalueer. Vir sulke tegnieke word die rekonstruksie van die aantrekker in fase-ruimte geassosieer met die tydreeks gewoonlik vereis. Inbedmetodes word aangebied as 'n manier om die aantrekker te rekonstrueer uit beperkte data. Metodes om die minimum inbed-dimensie te bereken uit gemiddelde wedersydse inligting sowel as die optimale tydsvertraging te bereken uit vals-buurpunt-heuristiek, word bespreek. Die eerste voorspellingsalgoritme wat bespreek word is gebaseer op 'n tegniek van Sauer. Hierdie algoritme maak gebruik van die implementering van singulierwaarde-ontbinding van die ingebedde tydreeks wat voorspel word. Die tweede voorspellingsalgoritme is gebaseer op neurale netwerke. 'n Spesifieke netwerkargitektuur geskik vir deterministiese chaotiese tydreekse, naamlik die tydafhanklike neurale netwerk argitektuur word bespreek en ge"implementeer. 'n Modifikasie van die terugprapagerende leer-algoritme vir gebruik met die tydafhanklike neurale netwerk word ook aangebied. Albei algoritmes word geevalueer deur voorspellings te maak vir die bekende Lorenz tydreeks. Verskeie inbed parameters en ander algoritme-spesifieke parameters word gebruik om die voorspelling te maak. Die werklike waardes vanuit die Lorentz tydreeks word gebruik om die voorspellings te evalueer en om voorspellingsakkuraatheid te bepaal. Die voorspelde tydreekse word geevalueer op grand van twee kriteria, naamlik voorspellingsakkuraatheid, en kwalitatiewe gedragsakkuraatheid. Gedragsakkuraatheid verwys na die vermoe van die algoritme om die kwalitatiewe eienskappe van die tydreeks korrek te simuleer. Daar word aangetoon dat vir beide algoritmes die keuse van inbed-dimensie grater as die minimum inbeddimensie soos bereken uit die vals-buurpunt-heuristiek, grater akkuraatheid gee. Vir die neurale netwerkalgoritme gee 'n inbed-dimensie grater as die minimum inbed-dimensie ook betel' gedragsakkuraatheid soos verwag. Vir Sauer se algoritme, egter, word betel' gedragsakkuraatheid gevind vir 'n inbed-dimensie kleiner as die minimale inbed-dimensie. In terme van tydsvertraging word dit aangetoon dat vir beide algoritmes die grootste voorspellingsakkuraatheid verkry word by tydvertragings in 'n interval rondom die optimale tydsvetraging. Daar word ook aangetoon dat die neurale netwerk-algoritme die beste gedragsakkuraatheid gee vir tydsvertragings naby aan die optimale tydsvertraging, terwyl Sauer se algoritme betel' gedragsakkuraatheid gee by kleineI' waardes van die tydsvertraging. Die Matlab kode van beide algoritmes word ook aangebied.

Thesis (MBA)--Stellenbosch University, 2000. / ENGLISH ABSTRACT: Continuous change has become one of the major characteristics of the South African manufacturing environment. Such an unstable dynamic environment, where continuous change is a normal occurrence, necessitates an appropriate response in order to regain or sustain competitive advantage. The environment is changing so fast that most small and medium manufacturing enterprises barely have the ability to survive the day-to-day challenges, without even seeing or thinking about the real challenges of surviving in the future, and more importantly, not only surviving, but actually prospering through these new challenges. The conventional approaches of strategic management do not satisfy the fast decision making requirements of today's organisations. The development of the different schools of strategic planning clearly shows how the strategic management process has developed with the changing times. One of the enduring problems facing the field of strategic management is the lack of theoretical tools available to describe and predict the behaviour of firms and industries. The fundamental problem is that industries evolve in a dynamic way over time as a result of complex interactions among firms, government, labour, financial institutions and other elements of the environment. These interactions are strategic in the sense that decisions by one party take into account anticipated reactions by others, and thus reflect recognition of interdependence. Existing models tend to assume relatively simple linear relationships without feedback. Chaos theory, which is the study of non-linear dynamic systems, promises to be a useful conceptual framework that reconciles the essential unpredictability of industries with the emergence of distinctive patterns. To understand the relevance of chaos theory to strategy, industries need to be conceptualised as complex, dynamic, non-linear systems. A basic strategic planning model was developed, incorporating some aspects of chaos theory, containing the following basic elements: vision, environmental scanning, strategic objectives, measurements, strategies and performance evaluation. The final aspects covered are some aspects of strategy implementation, concluding with some final notes confirming that one of the main reasons for strategic assessment of the organisation's situation is to exploit possible advantages from external, discontinuous changes and so gain first mover advantages by surprising the 'enemy'. To cope with chaos, a quickly responsive, organic corporation needs to be crafted. / AFRIKAANSE OPSOMMING: Een van die hoofkenmerke van die huidige Suid-Afrikaanse vervaardigingsomgewing is voortdurende verandering. Ten einde 'n mededingende voordeel in hierdie veranderende, dinamiese milieu te verkry en te behou, verg besondere vaardighede en innoverende tegnieke. Die meeste klein- en mediumgroot-ondernemings bevind hulself midde-in hierdie vinnig veranderende omgewing, waar hulle nie net daagliks moet oorleef nie, maar ook die uitdaging van langtermyn oorlewing die hoof moet bied. Ongelukkig vorm langtermynoorlewing en groei dikwels nie deel van meeste ondernemings se beplanning nie. Konvensionele benaderings tot strategiese beplanning kan nie meer die moderne onderneming se behoefte aan vinnige besluitneming bevredig nie. Die ontwikkeling van die verskillende denkskole oor strategiese beplanning toon ook 'n duidelike beweging in die rigting van sneller verandering in strategiese bestuur. Een van die probleme ten opsigte van strategiese bestuur, is die gebrek aan teoretiese modelle om die gedrag van ondernemings te beskryf en te voorspel. Die onderliggende probleem is egter dat ondernemings oor 'n lang tydperk groei en ontwikkel as deel van 'n komplekse interaksie met ander ondernemings, asook met die regering, arbeid, kapitaal en ander elemente binne die bedryf. Sodanige interaksie is van strategiese belang, aangesien 'n spesifieke rolspeler telkens antisipeer watter impak elke besluit wat geneem word, op die res van die omgewing gaan hê. Bestaande teoretiese modelle impliseer relatief eenvoudige, lineêre verwantskappe wat geen terugvoer bied nie. Daarteenoor skep die sogenaamde chaosteorie, dit wil sê die studie van dinamiese, nie-lineêre stelsels, 'n konseptuele raamwerk met bepaalde patrone waarmee die onvoorspelbaarheid van ondernemings verklaar en beskryf kan word. Die relevansie van die chaosteorie vir strategiese beplanning en bestuur kan egter slegs begryp word indien ondernemings as komplekse, dinamiese, nie-lineêre stelsels beskou word. In hierdie studie is 'n basiese strategiese beplanningsmodel ontwikkel. Belangrike aspekte wat gedek is, is einddoel, omgewingstudie, strategiese doelwitte, meting, strategieë en prestasie-evaluering. Daar word ook kortliks gekyk na moontlike probleme om dié model te implementeer, met verwysings na die impak van chaosteorie op die tradisionele beplannings- en implementerings-modelle. Ter afsluiting word daar klem gelê op die geleenthede wat deur die snelveranderende omgewing geskep word, en die noodsaaklikheid daarvan dat 'n onderneming gereed moet wees om binne hierdie omgewing vinnig en effektief op te tree. Die kern van enige onderneming se sukses lê in sy vermoë om verandering raak te sien, geleenthede te identifiseer en onmiddellik daarop te reageer.

Faculty of Education. Includes bibliographical references (leaves 194-222)