Thesis (M. S.)--Physics, Georgia Institute of Technology, 2009. / Committee Chair: Cvitanovic, Predrag; Committee Member: Dieci, Luca; Committee Member: Grigoriev, Roman; Committee Member: Schatz, Michael; Committee Member: Wiesenfeld, Kurt

Thesis (Th. M.)--Calvin Theological Seminary, 1995. / Abstract. Includes bibliographical references (leaves 189-200).

Thesis (Ph. D.)--West Virginia University, 2000. / Title from document title page. Document formatted into pages; contains xi, 113 p. : ill. (some col.). Includes abstract. Includes bibliographical references.

Thesis (Ph.D.)--Aberdeen University, 2008. / Includes bibliographical references.

Thesis (Ph.D.)--University of Nebraska-Lincoln, 2006. / Title from title screen (sites viewed on August 11, 2006). PDF text of dissertation: xx, 160 p. : ill. ; 1.73Mb. UMI publication number: AAT 3208123. Includes bibliographical references. Also available in microfilm, microfiche and paper format.

Thesis (Ph. D.)(Industrial Engineering)--University of Pretoria, 2005. / Includes summary. Includes bibliographical references. Available on the Internet via the World Wide Web.

M.Ing. (Electrical And Electronic Engineering) / Please refer to full text to view abstract

2003 / Some important ideas froni classical control theory are introduced with the intention of applying them to chaotic dynamical systems, in particular the coupled logistic equations. The structure of this dissertation is such that a strong foundation in control theory is first established before introducing the coupled logistic map or the methods of control and targetting in chaotic systems. In chapter 1 some aspects of classical control theory are reviewed. Continuous- and discrete-time dynamical systems are introduced and the existence and uniquendss criteria for the continuous case are explored via Lipschitz continuity. The matrix form of an inhomogeneous linear differential equation is presented and several properties of the associated transition matrix are discussed. Several linear algebraic ideas, most notably the Cayley-Hamilton theorem, are employed to explore the important concepts of controllability and observability in linear systems. The stabilisability problem is thoroughly investigated. Finally, the neighbourhood properties of continuous nonlinear dynamical systems with reference to controllability, stability and noise are established. Chapter 2 places emphasis on canonical forms, pole assignments and state observers. The decomposition of a general system into distinct components is facilitated by the general structure theorem, which is proved. The pole placement problem is described and the correspondence between the stabilisability of a system and the placement of poles is noted by the use'of a socalled feedback matrix. Lastly, the notion of a state observer, with reference to some dynamic feedback law, is introduced. The dynamics of the coupled logistic equations are studied in chapter 3. The fixed points of the map are calculated and the subsequent dynamical consequences explored. Using methods introduced in earlier chapters, the stability of the map is investigated. Using the so-called variational equations, the Lyapunov exponents are computed and used to classify, the motion of the system for the parameter values r and a. This chapter concludes with a discussion of the basins of attraction and critical curves associated with the coupled logistic equations. It is in chapter 4 that the models for controlling chaos are instantiated. The famous Ott-Grebogi- Yorke (OGY) method for controlling chaos is explained and related to the pole placement problem, discussed previously. The theory is extended to study the control of periodic orbits with periods greater than one.

The theme of this masters thesis are driven chaotic oscillators. The aim of this project is show the various types of driven chaotic oscillator and propose mathematical model solutions using numerical methods. In the first part of this thesis are shown theory of chaos, history of chaos theory, chaotic systems and chaos quantifiers. Next is numerical analysis of differential equations second order by Runge-Kutta fourth order method. Next part contains circuit blocks and synthesis of oscillators. In next part are defined all types of oscillators. Parameters of analysis, equations, circuits and simulations are defined for each type of driven chaotic oscillators. In each subchapter is design electrical circuit. This circuit is simulated and some of them realized.

Although a closed quantum system lacks clear signatures of classical chaos, it has been shown numerically that correspondence between an open quantum system and open classical system can be established. This phenomenon is explored for the case of an unconditioned evolution, where a system interacts with its environment, but the environment does not extract any information. This has been dubbed the “weak” transition and stands in contrast to the “strong” version where information is extracted by the environment. The transition is numerically mapped for the classically chaotic Duffing oscillator. Closed quantum and classically chaotic systems fail to agree due to the presence of fine scale structure in the classical evolution and the abundance of nonlocal interference in the quantum evolution. We show how noise mitigates both of these effects by suppressing the foliation of the classical unstable manifold while simultaneously acting as a passive filter of nonlocal quantum interference. The predicted transition parameter values are tested numerically for the Duffing oscillator. Finally, we explore whether these mechanisms are responsible for the emergence of classical chaos. While they do modify closed system spectral arguments against chaotic behavior, they do not provide a signature of chaotic dynamics. This stands in contrast to the trajectory level chaos observed in the strong transition. Keywords: nonlinear dynamics, quantum-classical transition, theoretical physics