Thesis (M.S.)--Rochester Institute of Technology, 2009. / Typescript. Includes bibliographical references (leaves 41-43).

Dissertation (D.M.A.)--The University of North Carolina at Greensboro, 2009. / Directed by Kelly Burke; submitted to the School of Music. Title from PDF t.p. (viewed May 11, 2010). Includes bibliographical references (p. 148-159).

Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisors: Jack S. Turner and Dean J. Driebe. Vita. Includes bibliographical references and index.

Thesis (Ph. D.)--University of Sydney, 2008. / Includes graphs. Title from title screen (viewed November 28, 2008) Submitted in fulfilment of the requirements for the degree of Doctor of Philosophy to the School of Mathematics and Statistics, Faculty of Science. Includes bibliographical references. Also available in print form.

Ph.D. / The work presented in this dissertation is concerned with the application of Chaos Theory to the field of Electrical and Electronic Engineering. A comprehensive study on electrical and electronic systems which exhibit chaotic behaviour, forms an integral part of this work. The objective of this survey is, firstly, to assess how widely chaos occurs in the field of electrical engineering. Secondly, the survey attempts to determine how successfully chaotic behaviour (in electrical systems) is identified and characterized. Finally, the survey aims to determine to what extent nonlinear phenomena and specifically chaos is applied to solve engineering problems. From this survey it is concluded that the study of chaos in electronics has reached a mature state. Currently, research focuses on controlling chaos, finding new applications of chaos as well as using chaos theory to gain a better understanding of the nonlinear world we live in. The other component of this dissertation consists of research done in the field of electronics. Contributions are made in controlling chaos and the analysis of chaotic systems both analytically and numerically.

The process of psychological change is complex, mirroring the complexity of life (Mahoney, 1991). Such complexity is nonlinear. Essentially, people are nonlinear dynamical systems and are characterised by an ever-changing, ever-adaptive movement from one state of order to another. This movement is a sequential flux, a turbulent ebb and flow of forces and form. Psychological change, too, follows this chaotic process of change (Butz, 1997). This is in line with the ‘new science’ of complexity. A postmodern vision, this is an ecological worldview that sees the world in terms of wholeness, interconnectedness, context, and nonlinear process (Goerner, 1995a). Three fields characterised by and concerned with complexity and which embrace the postmodern, ecological worldview are constructivism, ecopsychology, and chaos theory. Constructivism holds that people are meaning-making individuals who construct their own versions of reality; people are proactive, self-organising, and ever adapting to higher levels of complexity (Masterpasqua & Perna, 1997; Neimeyer & Mahoney, 1995). Ecopsychology is a synthesis of psychology and ecology; it is inspired by a holistic version of reality and posits the mutual embeddedness of humans and nature, the systemic connectedness of all that exists, and the evolutionary flux of the universe (Goerner, 1995a; Metzner, 1999). Chaos theory is the face of complexity; it is concerned with nonlinear dynamic systems as they evolve over time and the patterns and processes underlying such change (Cambel, 1993; Kellert, 1993). Although individually powerful and relevant for psychology, these fields are highly fragmented and often impractical. Much potential lies in their integration. Against this background, two goals were pursued in this study: 1) primarily, to simply and clearly demonstrate the concepts and application of chaos theory in a therapeutic situation; 2) to integrate the fields of constructivism, ecopsychology, and chaos theory relevant to the main goal of the study. Constructivism served as a grounding epistemology and, within this, ecopsychology served as a context within which chaos theory was utilised as a therapeutic applicatory model. The grounding epistemology, integration, and intervention are premised on the notions that: a) nature and humans are mutually and crucially embedded in each other; b) nature is characterised by nonlinear dynamical systems and the chaotic process of change, and thus humans (ie: dynamical systems) are also necessarily subject to such natural laws and principles; c) humans are proactive and may utilise the principles of chaos theory – notably self-organisation – to consciously initiate their own chaotic process of psychological change. The fields of constructivism, ecopsychology, and chaos theory are characterised by new and innovative forms of research and design methods. Such a pioneering spirit underpinned this study. The emphasis was on simplicity and pragmatic utility, using down-to-earth methods geared to producing practical and relevant data for use in therapy. A prime consideration was to ground the study in real-life. An empirical, descriptive field study was thus used, utilising an intensive single-case quantitative (time-series) design for data collection and a qualitative analysis. The intervention was aimed at initiating and facilitating psychological change, and was conducted with three participants. A nature-based metaphor and related guided imagery were used as a structure for the intervention. The intervention was conducted over three months. Participants completed self-report scales four times daily for the duration of the intervention, yielding time-series data. Analysis was by means of interpretation of three-dimensional geometric phase portraits and time-series graphs. Interpretations were used heuristically, triangulating them with clinical observations and verbal feedback from participants. Results showed that each of the three participants changed psychologically in different ways in the intervention, with certain aspects of chaos theory more applicable to one or the other. Considered together, the data pertaining to the three participants were clearly related to the principles of chaotic change. It was concluded that the concepts of chaos theory were shown to be relevant for therapy and that their application could be demonstrated simply and clearly. Chaos theory holds much potential as an applicatory model in psychology and would be well served by the use of more simple and pragmatic research methods. The use of triangulation in chaos theory analysis was found to be a particularly powerful methodology. The integration of constructivism, ecopsychology, and chaos theory proved to be a powerful framework for therapy and holds much potential for future development as a framework for broader psychological investigation and application. Much future research could be pursued from where this study leaves off. More studies focusing on simple and clear applications of chaos theory in therapy could be undertaken. Practical studies conducted in real-life therapeutic situations using innovative methodology would be particularly useful. A more comprehensive integration of constructivism, ecopsychology, and chaos theory could be undertaken. This could be a rich synthesis, going beyond unification of the core fundamentals to consider more widely related aspects of therapy and psychology. / Professor Gertie Pretorius

The phenomenon of dynamically induced anomalous diffusion is both the classical and quantum kicked rotor is investigated in this dissertation. We discuss the capability of the quantum mechanical version of the system to reproduce for extended periods the corresponding classical chaotic behavior.

This thesis investigates the relationship between semantic change and theory change in science. The study focuses on thirty years of developments in chaos theory. Because of measurement problems associated with certain nonlinear phenomena, the observability of chaotic systems is severely limited. In such cases, ongoing processes of language change may play a greater role in shaping scientific theories than in cases in which the phenomena are more easily observed. This study is interdisciplinary, drawing on theories from linguistics, philosophy, philology, and sociology. Several mechanisms of semantic change are explored in order to discover their possible influence on theory formation. Developments in chaos theory are described in terms of George Lakoff's radial model of conceptual categories. This model describes concepts in terms of (1) a central cluster which acts as a prototypical example, and (2) various non-central extensions from that center. I argue that in an emerging discipline, non-central extensions are made depending on the interests of the community. As Andrew Pickering observed, communities on the research front select a research direction that will intersect with the interests of more established research communities. This thesis explores several examples of historical developments in chaos research showing how conceptual change in science can be described in terms of Lakoff' s radial category model and Pickering's interest model. / Master of Science

A pendulum with its supporting point vibrating in both the x and the y direction is analyzed. Numerical simulation by computer is used to analyze the motion of the pendulum. Chaotic motion of the system is observed. Threshold values for chaos are obtained by simulation. The Lyapunov exponent and the fast Fourier transform ( FFT ) are used as the criteria to determine if the system is chaotic. Two predictive theoretical criteria, the Melnikov criterion and a period-doubling criterion, are then applied to the system. The results obtained by simulation and by theoretical criteria are shown to be in good agreement. A brute-force approach is used to supplement the results. It is found that the motion of this simple driven pendulum will have very complicated behavior. Multiple attractors can be shown to coexist. / Master of Science

published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy