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Dissertations / Theses on the topic 'Chaotic behavior in systems'

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Published: 4 June 2021

Last updated: 29 July 2024

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1

Michaels, Alan Jason. "Digital chaotic communications." Diss., Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/34849.

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This dissertation provides the conceptual development, modeling and simulation, physical implementation, and measured hardware results for a practicable digital coherent chaotic communication system. Such systems are highly desirable for robust communications due to the maximal entropy signal characteristics that satisfy Shannon's ideal noise-like waveform and provide optimal data transmission across a flat communications channel. At the core of the coherent chaotic communications system is a fully digital chaotic circuit, providing an efficiently controllable mechanism that overcomes the traditional bottleneck of chaotic circuit state synchronization. The analytical, simulation, and hardware results yield a generalization of direct sequence spread spectrum waveforms, that can be further extended to create a new class of maximal entropy waveforms suitable for optimized channel performance, maximal entropy transmission of chaotically spread amplitude modulated data constellations, and permission-based multiple access systems.

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2

Çek, Mehmet Emre Savacı Ferit Acar. "Analysis of observed chaotic data/." [s.l.]: [s.n.], 2004. http://library.iyte.edu.tr/tezler/master/elektronikvehaberlesme/T000493.rar.

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3

Çiftçi, Mahmut. "Channel equalization for chaotic communications systems." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/15464.

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4

Carlu, Mallory. "Instability in high-dimensional chaotic systems." Thesis, University of Aberdeen, 2019. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?pid=240675.

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In this thesis I make extensive use of the Lyapunov analysis formalism to unravel fundamental mechanisms of instability in two diﬀerent systems : the Kuramoto model of globally coupled phase-oscillators and the Lorenz 96 (L96) atmospheric "toy" model, portraying the evolution of a physical quantity along a latitude circle. I start by introducing the relevant theoretical background, with special attention on the main tools I have been using throughout this work : Lyapunov Exponents (LEs), which quantify the asymptotic growth rates of inﬁnitesimal perturbations in a system, and by extension, its degree of chaoticity, and Covariant Lyapunov Vectors (CLVs), which indicate the phase space direction (or the geometry) associated with these growth rates. The Kuramoto model is central in the study of synchronization among oscillatory units characterized by their various natural frequencies, but little is known on its chaotic dynamics in the unsynchronized state. I thus investigate the scaling behavior of the ﬁrst LE, upon diﬀerent assumptions on the natural frequencies, and make use of educated structural simpliﬁcations to analyze the origin of chaos in the ﬁnite size model. On the other hand, the L96 model has been devised to gather the main dynamical ingredients of atmospheric dynamics, namely advection, damping, external (solar) forcing and transfers across diﬀerent scales of motion, in a minimalist and functional way. It features two coupled dynamical layers : the large scale variables, representing synoptic scale atmospheric dynamics, and the small scale variables, faster and more numerous, associated with convective scale dynamics. The core of the study revolves around geometrical properties of CLVs, in the aim of understanding the processes underlying the observed multiscale chaoticity, and an exhaustive study of a non-trivial ensemble of CLVs featuring relevant projection on the slow subspace.

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5

Reiss, Joshua D. "The analysis of chaotic time series." Diss., Full text available online (restricted access), 2001. http://images.lib.monash.edu.au/ts/theses/reiss.pdf.

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6

Ghofranih, Jahangir. "Control and estimation of a chaotic system." Thesis, University of British Columbia, 1990. http://hdl.handle.net/2429/29601.

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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

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7

Cromwell, Jeff B. "Chaotic price dynamics of agricultural commodities." Morgantown, W. Va. : [West Virginia University Libraries], 2004. https://etd.wvu.edu/etd/controller.jsp?moduleName=documentdata&jsp%5FetdId=3625.

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Thesis (Ph. D.)--West Virginia University, 2004.
Title from document title page. Document formatted into pages; contains vi, 166 p. : ill. Includes abstract. Includes bibliographical references (p. 142-160).

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8

Lindquist, Roslyn Gay. "The dimension of a chaotic attractor." PDXScholar, 1991. https://pdxscholar.library.pdx.edu/open_access_etds/4182.

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Tools to explore chaos are as far away as a personal computer or a pocket calculator. A few lines of simple equations in BASIC produce fantastic graphic displays. In the following computer experiment, the dimension of a strange attractor is found by three algorithms; Shaw's, Grassberger-Procaccia's and Guckenheimer's. The programs were tested on the Henon attractor which has a known fractal dimension. Shaw's and Guckenheimer's algorithms were tested with 1000 data points, and Grassberger's with 100 points, a data set easily handled by a PC in one hour or less using BASIC or any other language restricted to 640K RAM. Since dimension estimates are notorious for requiring many data points, the author wanted to find an algorithm to quickly estimate a low-dimensional system (around 2). Although all three programs gave results in the neighborhood of the fractal dimension for the Henon attractor, Dfracta1=1.26, none appeared to converge to the fractal dimension.

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9

Fleming-Dahl, Arthur. "A chaotic communication system with a receiver estimation engine." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/15651.

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10

Akguc, Gursoy Bozkurt. "Chaos in 2D electron waveguides." Access restricted to users with UT Austin EID Full text (PDF) from UMI/Dissertation Abstracts Internaional, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3035928.

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11

Bishop, Robert Charles. "Chaotic dynamics, indeterminacy and free will /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.

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12

Ye, Shuang. "Electrical chaoization and its application in industrial mixing." Click to view the E-thesis via HKUTO, 2007. http://sunzi.lib.hku.hk/HKUTO/record/B39559051.

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13

叶霜 and Shuang Ye. "Electrical chaoization and its application in industrial mixing." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2007. http://hub.hku.hk/bib/B39559051.

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14

Locquet, Alexandre Daniel. "Chaotic optical communications using delayed feedback systems." Available online, Georgia Institute of Technology, 2005, 2005. http://etd.gatech.edu/theses/available/etd-01102006-133806/.

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Thesis (Ph. D.)--Electrical and Computer Engineering, Georgia Institute of Technology, 2006.
Bertrand Boussert, Committee Member ; Douglas B. Williams, Committee Member ; William T. Rhodes, Committee Member ; Yves Berthelot, Committee Member ; David S. Citrin, Committee Chair.

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15

Constantine, William L. B. "Wavelet techniques for chaotic and fractal dynamics /." Thesis, Connect to this title online; UW restricted, 1999. http://hdl.handle.net/1773/7124.

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16

Drake, Daniel F. "Information's role in the estimation of chaotic signals." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/14793.

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17

VanWiggeren, Gregory D. "Chaotic communication with erbium-doped fiber ring lasers." Diss., Georgia Institute of Technology, 2000. http://hdl.handle.net/1853/30299.

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18

Glenn, Tracy A. "The recategorization of "chaos" : a case study of language change and theory change /." Thesis, This resource online, 1990. http://scholar.lib.vt.edu/theses/available/etd-11242009-020011/.

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19

Albert, Gerald (Gerald Lachian). "Synchronous Chaos, Chaotic Walks, and Characterization of Chaotic States by Lyapunov Spectra." Thesis, University of North Texas, 1993. https://digital.library.unt.edu/ark:/67531/metadc277794/.

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Four aspects of the dynamics of continuous-time dynamical systems are studied in this work. The relationship between the Lyapunov exponents of the original system and the Lyapunov exponents of induced Poincare maps is examined. The behavior of these Poincare maps as discriminators of chaos from noise is explored, and the possible Poissonian statistics generated at rarely visited surfaces are studied.

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20

Elston, Timothy G. "The effects on intrinsic fluctuations of chaotic dynamics." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/29440.

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21

Eidson, John Charles. "Chaotic dynamics of two-level atoms interacting with a radiation field." Diss., Georgia Institute of Technology, 1987. http://hdl.handle.net/1853/29876.

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22

Sun, Hongyan. "Coupled nonlinear dynamical systems." Morgantown, W. Va. : [West Virginia University Libraries], 2000. http://etd.wvu.edu/templates/showETD.cfm?recnum=1636.

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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.

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23

Meadows, Brian K. "Spatiotemporal dynamics of stochastic and chaotic arrays." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/30747.

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24

Oskay, Windell Haven. "Atom optics experiments in quantum chaos." Access restricted to users with UT Austin EID Full text (PDF) from UMI/Dissertation Abstracts International, 2001. http://wwwlib.umi.com/cr/utexas/fullcit?p3040634.

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25

Kim, Sukkeun. "Stochastic chaos and resonance in bistable systems /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.

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26

Bracikowski, Christopher. "Fluctuations and chaos in a multimode solid state laser system." Diss., Georgia Institute of Technology, 1991. http://hdl.handle.net/1853/30658.

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27

Black, Robert D. (Robert Douglas) Carleton University Dissertation Computer Science. "On fractals, chaos and the Hailstone numbers." Ottawa, 1992.

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28

Tse, Pak-hoi Isaac. "Dynamical systems theory and school change." Click to view the E-thesis via HKUTO, 2006. http://sunzi.lib.hku.hk/hkuto/record/B37626218.

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29

Tse, Pak-hoi Isaac, and 謝伯開. "Dynamical systems theory and school change." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B37626218.

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30

Lee, Chungyong. "Noise reduction methods for chaotic signals with application to secure communications." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/14823.

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31

Verdin, Berenice. "Characterization of high resolution range and Doppler chaotic ladar." To access this resource online via ProQuest Dissertations and Theses @ UTEP, 2009. http://0-proquest.umi.com.lib.utep.edu/login?COPT=REJTPTU0YmImSU5UPTAmVkVSPTI=&clientId=2515.

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32

Tsankov, Tsvetlin Draganov. "Topological aspects of the structure of chaotic attractors in R3̂ /." Philadelphia, Pa. : Drexel University, 2004. http://dspace.library.drexel.edu/handle/1860/304.

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33

Rogers, Jeffrey L. "Modulated pattern formation : stabilization, complex-order, and symmetry." Diss., Georgia Institute of Technology, 2001. http://hdl.handle.net/1853/30930.

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34

Rontani, Damien. "Communications with chaotic optoelectronic systems - cryptography and multiplexing." Diss., Georgia Institute of Technology, 2011. http://hdl.handle.net/1853/42810.

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With the rapid development of optical communications and the increasing amount of data exchanged, it has become utterly important to provide effective ar- chitectures to protect sensitive data. The use of chaotic optoelectronic devices has already demonstrated great potential in terms of additional computational security at the physical layer of the optical network. However, the determination of the security level and the lack of a multi-user framework are two hurdles which have prevented their deployment on a large scale. In this thesis, we propose to address these two issues. First, we investigate the security of a widely used chaotic generator, the external cavity semiconductor laser (ECSL). This is a time-delay system known for providing complex and high-dimensional chaos, but with a low level of security regarding the identification of its most critical parameter, the time delay. We perform a detailed analysis of the influence of the ECSL parameters to devise how higher levels of security can be achieved and provide a physical interpretation of their origin. Second, we devise new architectures to multiplex optical chaotic signals and realize multi-user communications at high bit rates. We propose two different approaches exploiting known chaotic optoelectronic devices. The first one uses mutually cou- pled ECSL and extends typical chaos-based encryption strategies, such as chaos-shift keying (CSK) and chaos modulation (CMo). The second one uses an electro-optical oscillator (EOO) with multiple delayed feedback loops and aims first at transpos- ing coded-division multiple access (CDMA) and then at developing novel strategies of encryption and decryption, when the time-delays of each feedback loop are time- dependent.

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35

Newell, Timothy C. (Timothy Charles). "Experimental Synchronization of Chaotic Attractors Using Control." Thesis, University of North Texas, 1994. https://digital.library.unt.edu/ark:/67531/metadc278971/.

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The focus of this thesis is to theoretically and experimentally investigate two new schemes of synchronizing chaotic attractors using chaotically operating diode resonators. The first method, called synchronization using control, is shown for the first time to experimentally synchronize dynamical systems. This method is an economical scheme which can be viably applied to low dimensional dynamical systems. The other, unidirectional coupling, is a straightforward means of synchronization which can be implemented in fast dynamical systems where timing is critical. Techniques developed in this work are of fundamental importance for future problems regarding high dimensional chaotic dynamical systems or arrays of mutually linked chaotically operating elements.

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36

Ge, Yuzhen. "Studies of one-dimensional unimodal maps in the chaotic regime." Diss., Virginia Tech, 1990. http://hdl.handle.net/10919/39904.

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For one-dimensional uninmodal maps hλ(x) a binary tree which includes all the periodic windows in the chaotic regime is constructed. By associating each element in the tree with the superstable parameter value of the corresponding periodic interval we define a different unimodal map. After applying a certain renormalization procedure to this new unimodal map, we find the period doubling fixed point g(x) which depends on the details of the map hλ(x) and the scaling constant α. The thermodynamics and the scaling function of the resulting dynamical system are also discussed. In addition, the total measure of the periodic windows is calculated with results in basic agreement with those obtained previously by Farmer. Up to 13 levels of the tree have been included, and the convergence of the partial sums of the measure is shown explicitly. It is conjectured that the asymptotic behavior of the partial sum of the measure as the number of levels goes to 00 is universal for the class of maps that have the same order of maximum. A new scaling law has been observed, i.e., the product of the length of a periodic interval characterized by sequence Q and the scaling constant of Q is found to be approximately 1. We also study two three-dimensional volume-preserving quadratic maps. There is no period doubling bifurcation in either case. We have also developed an algorithm to construct the symbolic alphabet for some given superstable symbolic sequences for one-dimensional unimodal maps. Using this symbolic alphabet and the approach of cycle expansion the topological entropy can be easily computed. Furthermore, the scaling properties of the measure of constant topological entropy are studied. Our results support the conjectures that for the maps with the same order of maximum, the asymptotic behavior of the partial sum of the measure as the level of the binary goes to infinity is universal and the corresponding 'fatness' exponent is universal. Numerical computations and analysis are also carried out for the clipped Bernoulli shift.
Ph. D.

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37

Wei, Chengeng. "Cusp singularity in nonlinear dynamical systems /." Philadelphia, Pa. : Drexel University, 2004. http://dspace.library.drexel.edu/handle/1860/287.

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38

Spear, Daniel. "Strange attractors." Diss., Online access via UMI:, 2007.

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39

Gregerson, David Lee. "An investigation of chaos in a single-degree-of-freedom slider-crank mechanism." Thesis, Georgia Institute of Technology, 1989. http://hdl.handle.net/1853/16805.

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40

Vega, José Luis. "Transition to chaos and its quantum manifestations." Diss., Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/30976.

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41

Kaplan, David Louis. "Characterizing chaos in a hybrid optically bistable device." Diss., The University of Arizona, 1988. http://hdl.handle.net/10150/184440.

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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.

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42

Ree, Suhan. "Studies of chaos in two-dimensional billiards /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.

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43

DERSTINE, MATTHEW WILLIAM. "OBSERVATION OF CHAOS IN A HYBRID OPTICAL BISTABLE DEVICE (PERIOD-DOUBLING)." Diss., The University of Arizona, 1985. http://hdl.handle.net/10150/187930.

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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.

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44

Yurchenko, Aleksey. "Some problems in the theory of open dynamical systems and deterministic walks in random environments." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26549.

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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.

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45

Paskauskas, Rytis. "Chaotic Scattering in Rydberg Atoms, Trapping in Molecules." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/19809.

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We investigate chaotic ionization of highly excited hydrogen atom in crossed electric and magnetic fields (Rydberg atom) and intra-molecular relaxation in planar carbonyl sulfide (OCS) molecule. The underlying theoretical framework of our studies is dynamical systems theory and periodic orbit theory. These theories offer formulae to compute expectation values of observables in chaotic systems with best accuracy available in given circumstances, however they require to have a good control and reliable numerical tools to compute unstable periodic orbits. We have developed such methods of computation and partitioning of the phase space of hydrogen atom in crossed at right angles electric and magnetic fields, represented by a two degree of freedom (dof) Hamiltonian system. We discuss extensions to a 3-dof setting by developing the methodology to compute unstable invariant tori, and applying it to the planar OCS, represented by a 3-dof Hamiltonian. We find such tori important in explaining anomalous relaxation rates in chemical reactions. Their potential application in Transition State Theory is discussed.

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46

Lan, Boon Leong. "Quantum-classical correspondence and quantum chaos in the periodically kicked pendulum." Diss., Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/27586.

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47

Ing, James. "Near grazing dynamics of piecewise linear oscillators." Thesis, Available from the University of Aberdeen Library and Historic Collections Digital Resources, 2008. http://digitool.abdn.ac.uk:80/webclient/DeliveryManager?application=DIGITOOL-3&owner=resourcediscovery&custom_att_2=simple_viewer&pid=24711.

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48

Cai, Qin. "Detecting Chaotic Signals with Nonlinear Models." PDXScholar, 1993. https://pdxscholar.library.pdx.edu/open_access_etds/4564.

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In this thesis we apply chaotic dynamic data analysis to the area of discrete time signal processing. A newly developed Hidden Filter Hidden Markov Model is introduced in detection of chaotic signals. Numerical experiments have verified that this novel nonlinear model outperforms linear AR model in detecting chaotic signals buried by noise having similar power spectra. A simple Histogram Model is proposed which can also be used to do detection on the data sets with chaotic behavior. Receiver Operating Characteristics for a variety of noise levels and model classes are reported.

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Mathew, Manu K. "Nonlinear system identification and prediction /." Online version of thesis, 1993. http://hdl.handle.net/1850/11594.

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50

In, Visarath. "Modification of nonlinear systems with chaos control and anticontrol." Diss., Georgia Institute of Technology, 1996. http://hdl.handle.net/1853/30898.

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