No description available.

Thesis (Ph. D.)--University of Hong Kong, 2008. / Also available in print.

Thesis (Master)--İzmir Institute of Technology, İzmir, 2004. / Includes bibliographical references (leaves. 86).

Thesis (M.S.)--Virginia Polytechnic Institute and State University, 1990. / Vita. Abstract. Includes bibliographical references (leaves 113-122). Also available via the Internet.

Thesis (Ph.D)--Mathematics, Georgia Institute of Technology, 2009. / Committee Chair: Bunimovich, Leonid; Committee Member: Bakhtin, Yuri; Committee Member: Cvitanovic, Predrag; Committee Member: Houdre, Christian; Committee Member: Weiss, Howard. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (M.C.S.)--Carleton University, 1992. / Also available in electronic format on the Internet.

Thesis (doctoral)--Universiteit Leiden, 2003. / Stellingen (2 p.) inserted.

A class of deterministic nonlinear systems known as ”chaotic” behaves similar to noise-corrupted systems. As a specific example, Duffing equation, a nonlinear oscillator representing the roll dynamics of a vessel, was chosen for the study. State estimation and control of such systems in the presence of measurement noise is the prime goal of this research. A nonlinear estimation suitable for chaotic systems was evaluated against conventional methods based on linear equivalent model, and proved to be very efficient. A state feedback controller and a sliding mode controller were applied to the chaotic system and both techniques provided satisfactory results. Investigating the persistence of chaotic behavior of the controlled system is a secondary goal. Simulation results showed that the chaotic behavior persisted in case of the linear feedback controller, while in case of the sliding mode controller the system did not exhibit any chaotic behavior. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

Turbulence and periodic oscillations are easily seen with an optically bistable device with a delay in the feedback. The device is a hybrid, having both optical and electronic components. The details of the time-dependent output are investigated. In particular, as the input intensity is increased, the device output goes through a series of second-order nonequilibrium phase transitions or bifurcations. A truncated period-doubling sequence is observed prior to the onset of turbulence or chaos. The truncation is shown to be due to a noise-induced bifurcation gap. Within the chaotic regime, the device largely follows the reverse bifurcation scheme of Lorenz. In addition, there is a small domain of frequency-locked behavior that exists within the chaotic domain. These frequency-locked waveforms represent an alternate path to chaos. With the route to choas well understood, it remained to characterize the erratic motion itself. Dimension and correlation entropy are measured for various settings of our hybrid device. The measured dimension is found to be significantly less than dimensions consistent with a conjecture due to Kaplan and Yorke. The standard method of determining correlation entropy is shown to yield more than one value.

An analog of an optically bistable device made constructed from both optical and electronic components is used to study chaos. This hybrid optically bistable system has a delay in the feedback so that the response time of the electronics is much faster than the feedback time. Such a system is unstable and shows pulsations and chaos. The character of the pulsations change as the gain of the amplifier or the input laser power is increased. These changes make up the period doubling route to chaos. Not all of the waveforms of an ideal period doubling sequence are observed. This truncation of the period-doubling sequence in the device is investigated as a function of the noise present in the system. Increasing the noise level decreases the number of period doublings observed. In the chaotic regime waveforms other than those predicted are observed. These waveforms are the frequency-locked waveforms seen in an earlier experiment which we find to be modified versions of the typical period-doubled waveforms. The transitions between these waveforms are discontinuous, and show hysteresis loops. By the introduction of an external locking signal, we are able to stabilize waveforms in the neighborhood of the discontinuous transitions. By so doing we show that the transitions among the branches are due to their lack of stability. The transitions are thus not strictly first-order nonequilibrium phase transitions, since in that case the branches cease to exist at the transition point. Since the path to chaos is nonunique, the types of chaos that are observable are also nonunique. To suggest a way to distinguish between different types of chaos and also to provide a tool for the study of chaos in other systems, we propose an operational test for chaos which leads to a straightforward experimental distinction between chaos and noise. We examine this test using the hybrid device to show that the method works. The test involves repeated measurement of the initial transient of a system whose initial condition is fixed. This method could be used to determine the existence of chaos in faster optical systems.