Stability analysis of networked dynamical systems has been of interest in many disciplines such as biology and physics and chemistry with applications such as LASER cooling and plasma stability. These large networks are often modeled to have a completely random (Erdös-Rényi) or semi-random (Small-World) topologies. The former model is often used due to mathematical tractability while the latter has been shown to be a better model for most real life networks. The recent emergence of cyber physical systems, and in particular the smart grid, has given rise to a number of engineering questions regarding the control and optimization of such networks. Some of the these questions are: How can the stability of a random network be characterized in probabilistic terms? Can the effects of network topology and system dynamics be separated? What does it take to control a large random network? Can decentralized (pinning) control be effective? If not, how large does the control network needs to be? How can decentralized or distributed controllers be designed? How the size of control network would scale with the size of networked system? Motivated by these questions, we began by studying the probability of stability of synchronization in random networks of oscillators. We developed a stability condition separating the effects of topology and node dynamics and evaluated bounds on the probability of stability for both Erdös-Rényi (ER) and Small-World (SW) network topology models. We then turned our attention to the more realistic scenario where the dynamics of the nodes and couplings are mismatched. Utilizing the concept of ε-synchronization, we have studied the probability of synchronization and showed that the synchronization error, ε, can be arbitrarily reduced using linear controllers. We have also considered the decentralized approach of pinning control to ensure stability in such complex networks. In the pinning method, decentralized controllers are used to control a fraction of the nodes in the network. This is different from traditional decentralized approaches where all the nodes have their own controllers. While the problem of selecting the minimum number of pinning nodes is known to be NP-hard and grows exponentially with the number of nodes in the network we have devised a suboptimal algorithm to select the pinning nodes which converges linearly with network size. We have also analyzed the effectiveness of the pinning approach for the synchronization of oscillators in the networks with fast switching, where the network links disconnect and reconnect quickly relative to the node dynamics. To address the scaling problem in the design of distributed control networks, we have employed a random control network to stabilize a random plant network. Our results show that for an ER plant network, the control network needs to grow linearly with the size of the plant network.

Bifurcations in Huang's chaotic chemical reactor system leading from simple dynamics into chaotic regimes are considered. Following the linear stability analysis, the periodic orbit resulting from a Hopf bifurcation of any of the six fixed points is constructed analytically by the method of multiple scales across successively slower time scales, and its stability is then determined by the resulting final secularity condition. Furthermore, we run numerical simulations of our chemical reactor at a particular fixed point of interest, alongside a set of parameter values that forces our system to undergo Hopf bifurcation. These numerical simulations then verify our analysis of the normal form.

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Exploring the concepts of long range aerial transport of microorganisms is the main motivation of this study. For this purpose we use theories and concepts of dynamical systems in the context of geophysical fluid systems. We apply powerful notions such as finite-time Lyapunov exponent (FTLE) and the associated Lagrangian coherent structures (LCS) and we attempt to provide mathematical explanations and frameworks for some applied questions which are based on realistic concerns of atmospheric transport phenomena. Accordingly, we quantify the accuracy of prediction of FTLE-LCS features and we determine the sensitivity of such predictions to forecasting parameters. In addition, we consider the spatiotemporal resolution of the operational data sets and we propose the concept of probabilistic source and destination regions which leads to the definition of stochastic FTLE fields. Moreover, we put forward the idea of using ensemble forecasting to quantify the uncertainty of the forecast results. Finally, we investigate the statistical properties of localized measurements of atmospheric microbial structure and their connections to the concept of local FTLE time-series. Results of this study would pave the way for more efficient models and management strategies for the spread of infectious diseases affecting plants, domestic animals, and humans. / Ph. D.

En esta Tesis se aborda la estimación óptima de señales caóticas generadas por mapas unidimensionales y contaminadas por ruido aditivo blanco Gaussiano, desde el punto de vista de los dos marcos de inferencia estadística más extendidos: máxima verosimilitud (ML) y Bayesiano. Debido al elevado coste computacional de estos estimadores, se proponen asimismo diversos estimadores subóptimos, aunque computacionalmente eficientes, con un rendimiento similar al de los óptimos. Adicionalmente se analiza el problema de la estimación de los parámetros de un mapa caótico explotando la relación conocida entre muestras consecutivas de la secuencia caótica. Por último, se considera la aplicación de los estimadores anteriores al diseño de receptores para dos esquemas de comunicaciones caóticas diferentes: conmutación caótica y codificación simbólica o caótica. / This Thesis studies the optimal estimation of chaoticsignals generated iterating unidimensional maps and contaminated by additive white Gaussian noise, from the point of view of the two most common frameworks in statistical inference: maximum likelihood (ML) and Bayesian. Due to the high computational cost of optimum estimators, several suboptimal but computationally efficient estimators are proposed, which attain a similar performance as the optimum ones. Additionally, the estimation of the parameters of a chaotic map is analyzed, exploiting the known relation between consecutive samples of the chaotic sequence. Finally, we consider the application of the estimators developed in the design of receivers for two different schemes of chaotic communications: chaotic switching and symbolic or chaotic coding.

The neural net computer simulations which will be presented here are based on the acceptance of a set of assumptions that for the last twenty years have been expressed in the fields of information processing, neurophysiology and cognitive sciences. First of all, neural networks and their dynamical behaviors in terms of attractors is the natural way adopted by the brain to encode information. Any information item to be stored in the neural net should be coded in some way or another in one of the dynamical attractors of the brain and retrieved by stimulating the net so as to trap its dynamics in the desired item's basin of attraction. The second view shared by neural net researchers is to base the learning of the synaptic matrix on a local Hebbian mechanism. The last assumption is the presence of chaos and the benefit gained by its presence. Chaos, although very simply produced, inherently possesses an infinite amount of cyclic regimes that can be exploited for coding information. Moreover, the network randomly wanders around these unstable regimes in a spontaneous way, thus rapidly proposing alternative responses to external stimuli and being able to easily switch from one of these potential attractors to another in response to any coming stimulus.<p><p>In this thesis, it is shown experimentally that the more information is to be stored in robust cyclic attractors, the more chaos appears as a regime in the back, erratically itinerating among brief appearances of these attractors. Chaos does not appear to be the cause but the consequence of the learning. However, it appears as an helpful consequence that widens the net's encoding capacity. To learn the information to be stored, an unsupervised Hebbian learning algorithm is introduced. By leaving the semantics of the attractors to be associated with the feeding data unprescribed, promising results have been obtained in term of storing capacity. / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished

This thesis constitutes a narrative that explores an alternative meaning construction for the experience of loss. During the telling of this story, I consider the appropriateness of adopting the 'new paradigm' approach for this particular thesis, and the constructivist and social constructionist epistemological assumptions underlying such an approach. I delve into the use of 'self as researcher under this epistemological umbrella. This is followed by an exploration of 'chaos theory' and its application to social systems. And finally, I consider the usefulness of this theory in constructing meanings for loss experiences on various systemic levels within my own family system. / Psychology / M.A.(Clinical Psychology)

The concept of strategy has advanced significantly from when the emphasis fell on comprehensive, systematic and rational planning. However, many of the assumptions that were embedded in traditional strategy models were deemed to be inadequate and outdated as we approached a new competitive milieu (Maritz, 2010). Strategic Management is still a comparatively young field and the existing toolbox of concepts and techniques remains woefully inadequate (Grant, 2010). This reality should force a re-examination of the traditional strategy paradigms (Maritz, 2010). The literature review has confirmed the observations by Maritz (2010) and Grant (2010) that indeed current strategic management paradigms or approaches were inadequate for unique business environments obtaining in a developing country in Africa, such as Zimbabwe. The motivation for this research, therefore, was to identify and recommend strategic management approaches or paradigms applicable to banks operating in a turbulent and chaotic environment. Based on an extensive literature review, in-depth interviews were conducted with six commercial banks (three that survived the turbulence and three that failed) during the period under review. The study established that the banks that survived the turbulence had a different strategic management approach from the traditional designed ones. It was also noted in this study that in turbulent environments, strategy-making is birthed through an emergent process. When events are moving at an unprecedented speed, as was happening in Zimbabwe, the time intervals between obtaining information, analysing information, taking decisions and implementing those decisions need to be tightly compressed. The researcher coined this process Strategic Intensity (SI). On the other hand, diversification as a strategy was found to be very risky for businesses that did not have a strong foundation and that were lacking in the appreciation of the risk complexion of the businesses into which they were diversifying. This research makes a significant contribution by identifying and recommending Strategic Management approaches applicable to businesses operating in a turbulent and chaotic environment in developing markets such as Zimbabwe. Furthermore, this research also contributes towards the current debate in academic literature amongst practitioners of strategy, about how strategy is really made in organisations (Maritz, 2010). The debate centres around two opposing views: one associated with strategy-making as a formal, deliberate plan, and the other associated with strategies as evolving, ever-changing sets of outcomes that are eventually realised. Finally, the researcher proposes that further studies be conducted at the end of this study. / Business Management / DBL