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Dissertations / Theses on the topic 'Chaotický systém'

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Published: 28 June 2021

Last updated: 13 February 2022

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1

Rujzl, Miroslav. "Analýza a obvodové realizace speciálních chaotických systémů." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2021. http://www.nusl.cz/ntk/nusl-442418.

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This master‘s thesis deals with analysis of electronic dynamical systems exhibiting chaotic solution. In introduction, some basic concepts for better understanding of dynamical systems are explained. After introduction, current knowledge from the world of circuits exhibiting chaotic solutions are discussed. The best-known chaotic systems are analyzed numerically in Matlab software. Numerical analysis and experimental verification were demonstrated at C class transistor amplifier, which confirmed the chaotic behavior and generation of a strange attractor.

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2

Khůlová, Jitka. "Stabilita a chaos v nelineárních dynamických systémech." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2018. http://www.nusl.cz/ntk/nusl-392836.

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Diplomová práce pojednává o teorii chaotických dynamických systémů, speciálně se pak zabývá Rösslerovým systémem. Kromě standardních výpočtů spojených s bifurkační analýzou se práce zaměřuje na problém stabilizace, konkrétně na stabilizaci rovnovážných bodů. Ke stabilizaci je využita základní metoda zpětnovazebního řízení s časovým zpožděním. Významnou část práce tvoří zavedení a implementace obecné metody pro hledání vhodné volby parametrů vedoucí k úspěšné stabiliaci. Dalším diskutovaným tématem je možnost synchronizace dvou Rösslerových systémů pomocí různých synchronizačních schémat.

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3

Schneider, Judith. "Dynamical structures and manifold detection in 2D and 3D chaotic flows." Phd thesis, [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=973637420.

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4

Borkovec, Ondřej. "Synchronizace chaotických dynamických systémů." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2019. http://www.nusl.cz/ntk/nusl-401496.

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Diplomová práce pojednává o chaotických dynamických systémech se zvláštním zaměřením na jejich synchronizaci. Proces synchronizace je aplikován použitím dvou různých metod, a to - metodou úplné synchronizace na dva Lorenzovy systémy a metodou negativní zpětné vazby na dva Rösslerovy systémy. Dále je prozkoumána možná aplikace synchronizace chaotických systémů v oblasti soukromé komunikace, která je doplněná algoritmy v prostředí MATLAB.

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5

Che, Dzul-Kifli Syahida. "Chaotic dynamical systems." Thesis, University of Birmingham, 2012. http://etheses.bham.ac.uk//id/eprint/3410/.

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In this work, we look at the dynamics of four different spaces, the interval, the unit circle, subshifts of finite type and compact countable sets. We put our emphasis on chaotic dynamical system and exhibit sufficient conditions for the system on the interval, the unit circle and subshifts of finite type to be chaotic in three different types of chaos. On the interval, we reveal two weak conditions’s role as a fast track to chaotic behavior. We also explain how a strong dense periodicity property influences chaotic behavior of dynamics on the interval, the unit circle and subshifts of finite type. Finally we show how dynamics property of compact countable sets effecting the structure of the sets.

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6

Karavas, Costas. "Fractal chaotic systems : investigation of the geological system and its sedimentation behaviour." Thesis, McGill University, 1990. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=60052.

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Chaos theory has only recently been related to various phenomena in the earth sciences. Here, using systems theory in a description of geological processes, we study the chaotic development of sedimentary sequences.
The geosystem is treated as a partially specified system in order to apply qualitative stability analysis in the investigation of sedimentation behaviour and interactions among geological processes. The analysis suggests that the sedimentary system is unstable. This instability in conjunction with the system's sensitive dependence to internal fluctuations (i.e., those generated within the system) provide supporting evidence to suggest a chaotic behaviour for the sedimentation system.
We suggest that chaos could act as the common underlying mechanism which is manifest as the fractal-flicker noise character observed in reflectivity well logs. Acoustic impedance variations--the geophysical measures of lithologic variability--represent the internal organization of the interacting geological processes. This organization under a chaotic regime is responsible for the common statistical character found in various sedimentary basins.

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7

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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8

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

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9

Baek, Seung-Jong. "Synchronization in chaotic systems." College Park, Md.: University of Maryland, 2007. http://hdl.handle.net/1903/7728.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2007.
Thesis research directed by: Dept. of Electrical and Computer Engineering. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

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10

Tang, Xian Zhu. "Transport in chaotic systems." W&M ScholarWorks, 1996. https://scholarworks.wm.edu/etd/1539623882.

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This dissertation addresses the general problem of transport in chaotic systems. Typical fluid problem of the kind is the advection and diffusion of a passive scalar. The magnetic field evolution in a chaotic conducting media is an example of the chaotic transport of a vector field. In kinetic theory, the collisional relaxation of a distribution function in phase space is also an advection-diffusion problem, but in a higher dimensional space.;In a chaotic flow neighboring points tend to separate exponentially in time, exp({dollar}\omega t{dollar}) with {dollar}\omega{dollar} the Liapunov exponent. The characteristic parameter for the transport of a scalar in a chaotic flow is {dollar}\Omega\ \equiv\ \omega L\sp2/D{dollar} where L is the spatial scale and D is the diffusivity. For {dollar}\Omega\ \gg\ 1{dollar}, the scalar is advected with the flow for a time {dollar}t\sb{lcub}a{rcub}\ \equiv{dollar} ln(2{dollar}\Omega{dollar})/2{dollar}\omega{dollar} and then diffuses during the relatively short period 1/{dollar}\omega{dollar} centered on the time {dollar}t\sb{lcub}a{rcub}{dollar}. This rapid diffusion occurs only along the field line of the {dollar}\rm \ s\sb\infty{dollar} vector, which defines the stable direction for neighboring streamlines to converge. Diffusion is impeded at the sharp bends of an {dollar}\rm \ s{dollar} line because of a peculiarly small finite time Lyapunov exponent, hence a class of diffusion barriers is created inside a chaotic sea. This result comes from a fundamental relationship between the finite time Lyapunov exponent and the geometry of the {dollar}\rm \ s{dollar} lines, which we rigorously show in 2D and numerically validated for 3D flows.;The evolution of a general 3D magnetic field in a highly conducting chaotic media is also related to the spatial-temporal dependence of the finite time Lyapunov exponent. The Ohmic dissipation in a chaotic plasma will become a dominate process despite a small plasma resistivity. We show that the Ohmic heating in a chaotic plasma occurs in current filaments or current sheets. The particular form is determined by the time dependence of spatial gradient of the finite time Lyapunov exponent along a direction in which neighboring point neither diverge nor converge.

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11

Kateregga, George William. "Bifurcations in a chaotic dynamical system." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2019. http://www.nusl.cz/ntk/nusl-401527.

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Dynamical systems possess an interesting and complex behaviour that have attracted a number of researchers across different fields, such as Biology, Economics and most importantly in Engineering. The complex and unpredictability of nonlinear customary behaviour or the chaotic behaviour, makes it strange to analyse them. This thesis presents the analysis of the system of nonlinear differential equations of the so--called Lu--Chen--Cheng system. The system has similar dynamical behaviour with the famous Lorenz system. The nature of equilibrium points and stability of the system is presented in the thesis. Examples of chaotic dynamical systems are presented in the theory. The thesis shows the dynamical structure of the Lu--Chen--Cheng system depending on the particular values of the system parameters and routes to chaos. This is done by both the qualitative and numerical techniques. The bifurcation diagrams of the Lu--Chen--Cheng system that indicate limit cycles and chaos as one parameter is varied are shown with the help of the largest Lyapunov exponent, which also confirms chaos in the system. It is found out that most of the system's equilibria are unstable especially for positive values of the parameters $a, b$. It is observed that the system is highly sensitive to initial conditions. This study is very important because, it supports the previous findings on chaotic behaviours of different dynamical systems.

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12

Vavriv, Dmytro. "Chaotic instabilities and their applications." Göttingen Cuvillier, 2009. http://d-nb.info/998762474/04.

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13

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

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14

Schäfer, Rudi. "Correlation functions and fidelity decay in chaotic systems." [S.l. : s.n.], 2004. http://archiv.ub.uni-marburg.de/diss/z2004/0660/.

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15

Weibert and Kirsten. "Semiclassical quantization of integrable and chaotic billiard systems by." Phd thesis, Universitaet Stuttgart, 2001. http://elib.uni-stuttgart.de/opus/volltexte/2001/815/index.html.

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16

Bäcker, Arnd. "Eigenfunctions in chaotic quantum systems." Doctoral thesis, Saechsische Landesbibliothek- Staats- und Universitaetsbibliothek Dresden, 2008. http://nbn-resolving.de/urn:nbn:de:bsz:14-ds-1213275874643-50420.

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The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted.

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17

Wiklund, Kjell Ottar. "Multifractal properties of chaotic systems." Thesis, Imperial College London, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338772.

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18

Bernhard, Michael A. "Introduction to chaotic dynamical systems." Thesis, Monterey, California. Naval Postgraduate School, 1992. http://hdl.handle.net/10945/23708.

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The emerging discipline known as "chaos theory" is a relatively new field of study with a diverse range of applications (economics, biology, meteorology, etc.). Despite this, there is not as yet a universally accepted definition for "chaos" as it applies to gen- eral dynamical systems. Various approaches range from topological methods of a qualitative description, to physical notions of randomness, information, and entropy in crgodic theory, to the development of computational definitions and algorithms designed to obtain quantitative information. This thesis develops some of the current definitions and discusses several quantita- tive measures of chaos. It is intended to stimulate the interest of undergraduate and graduate students and is accessible to those with a knowledge of advanced calculus and ordinary differential equations. In covering chaos for continuous systems it serves as a complement to the work done by Philip Beaver [Ref. 1], which details chaotic dynamics for discrete systems.

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19

Santoboni, Giovanni. "Synchronisation of coupled chaotic systems." Thesis, University College London (University of London), 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.391672.

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20

Xu, Daolin. "Flexible control of chaotic systems." Thesis, University College London (University of London), 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.338926.

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21

Bäcker, Arnd. "Eigenfunctions in chaotic quantum systems." Doctoral thesis, Technische Universität Dresden, 2007. https://tud.qucosa.de/id/qucosa%3A23663.

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The structure of wavefunctions of quantum systems strongly depends on the underlying classical dynamics. In this text a selection of articles on eigenfunctions in systems with fully chaotic dynamics and systems with a mixed phase space is summarized. Of particular interest are statistical properties like amplitude distribution and spatial autocorrelation function and the implication of eigenfunction structures on transport properties. For systems with a mixed phase space the separation into regular and chaotic states does not always hold away from the semiclassical limit, such that chaotic states may completely penetrate into the region of the regular island. The consequences of this flooding are discussed and universal aspects highlighted.

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22

Polo, Fabrizio. "Equidistribution on Chaotic Dynamical Systems." The Ohio State University, 2011. http://rave.ohiolink.edu/etdc/view?acc_num=osu1306527005.

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23

Frisk, Martin. "Synchronization in chaotic dynamical systems." Thesis, Uppsala universitet, Tillämpad matematik och statistik, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-287624.

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24

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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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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26

Kraut, Suso. "Multistable systems under the influence of noise." Phd thesis, [S.l.] : [s.n.], 2001. http://pub.ub.uni-potsdam.de/2002/0011/kraut.pdf.

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27

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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28

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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29

Eckstein, Bernd. "Bandcounter: Counting bands of multiband chaotic attractors." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2006. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-28244.

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30

Clodong, Sébastien. "Recurrent outbreaks in ecology chaotic dynamics in complex networks /." [S.l. : s.n.], 2004. http://pub.ub.uni-potsdam.de/2004/0062/clodong.pdf.

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31

Mulansky, Mario. "Chaotic diffusion in nonlinear Hamiltonian systems." Phd thesis, Universität Potsdam, 2012. http://opus.kobv.de/ubp/volltexte/2013/6318/.

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This work investigates diffusion in nonlinear Hamiltonian systems. The diffusion, more precisely subdiffusion, in such systems is induced by the intrinsic chaotic behavior of trajectories and thus is called chaotic diffusion''. Its properties are studied on the example of one- or two-dimensional lattices of harmonic or nonlinear oscillators with nearest neighbor couplings. The fundamental observation is the spreading of energy for localized initial conditions. Methods of quantifying this spreading behavior are presented, including a new quantity called excitation time. This new quantity allows for a more precise analysis of the spreading than traditional methods. Furthermore, the nonlinear diffusion equation is introduced as a phenomenologic description of the spreading process and a number of predictions on the density dependence of the spreading are drawn from this equation. Two mathematical techniques for analyzing nonlinear Hamiltonian systems are introduced. The first one is based on a scaling analysis of the Hamiltonian equations and the results are related to similar scaling properties of the NDE. From this relation, exact spreading predictions are deduced. Secondly, the microscopic dynamics at the edge of spreading states are thoroughly analyzed, which again suggests a scaling behavior that can be related to the NDE. Such a microscopic treatment of chaotically spreading states in nonlinear Hamiltonian systems has not been done before and the results present a new technique of connecting microscopic dynamics with macroscopic descriptions like the nonlinear diffusion equation. All theoretical results are supported by heavy numerical simulations, partly obtained on one of Europe's fastest supercomputers located in Bologna, Italy. In the end, the highly interesting case of harmonic oscillators with random frequencies and nonlinear coupling is studied, which resembles to some extent the famous Discrete Anderson Nonlinear Schroedinger Equation. For this model, a deviation from the widely believed power-law spreading is observed in numerical experiments. Some ideas on a theoretical explanation for this deviation are presented, but a conclusive theory could not be found due to the complicated phase space structure in this case. Nevertheless, it is hoped that the techniques and results presented in this work will help to eventually understand this controversely discussed case as well.
Diese Arbeit beschäftigt sich mit dem Phänomen der Diffusion in nichtlinearen Systemen. Unter Diffusion versteht man normalerweise die zufallsmäss ige Bewegung von Partikeln durch den stochastischen Einfluss einer thermodynamisch beschreibbaren Umgebung. Dieser Prozess ist mathematisch beschrieben durch die Diffusionsgleichung. In dieser Arbeit werden jedoch abgeschlossene Systeme ohne Einfluss der Umgebung betrachtet. Dennoch wird eine Art von Diffusion, üblicherweise bezeichnet als Subdiffusion, beobachtet. Die Ursache dafür liegt im chaotischen Verhalten des Systems. Vereinfacht gesagt, erzeugt das Chaos eine intrinsische Pseudo-Zufälligkeit, die zu einem gewissen Grad mit dem Einfluss einer thermodynamischen Umgebung vergleichbar ist und somit auch diffusives Verhalten provoziert. Zur quantitativen Beschreibung dieses subdiffusiven Prozesses wird eine Verallgemeinerung der Diffusionsgleichung herangezogen, die Nichtlineare Diffusionsgleichung. Desweiteren wird die mikroskopische Dynamik des Systems mit analytischen Methoden untersucht, und Schlussfolgerungen für den makroskopischen Diffusionsprozess abgeleitet. Die Technik der Verbindung von mikroskopischer Dynamik und makroskopischen Beobachtungen, die in dieser Arbeit entwickelt wird und detailliert beschrieben ist, führt zu einem tieferen Verständnis von hochdimensionalen chaotischen Systemen. Die mit mathematischen Mitteln abgeleiteten Ergebnisse sind darüber hinaus durch ausführliche Simulationen verifiziert, welche teilweise auf einem der leistungsfähigsten Supercomputer Europas durchgeführt wurden, dem sp6 in Bologna, Italien. Desweiteren können die in dieser Arbeit vorgestellten Erkenntnisse und Techniken mit Sicherheit auch in anderen Fällen bei der Untersuchung chaotischer Systeme Anwendung finden.

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32

Grant, Angela Elyse. "Finding optimal orbits of chaotic systems." College Park, Md. : University of Maryland, 2005. http://hdl.handle.net/1903/3220.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2005.
Thesis research directed by: Mathematics. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.

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Kohler, Heiner. "Group integrals in chaotic quantum systems." [S.l. : s.n.], 2000. http://deposit.ddb.de/cgi-bin/dokserv?idn=961274352.

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34

Williams, Christopher. "Chaotic synchronisation in wideband communication systems." Thesis, University of Bristol, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299732.

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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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Richard, Michael D. (Michael David). "Estimation and detection with chaotic systems." Thesis, Massachusetts Institute of Technology, 1994. http://hdl.handle.net/1721.1/12230.

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Thesis (Sc. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1994.
Includes bibliographical references (p. 209-214).
by Michael D. Richard.
Sc.D.

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37

Ramirez, Daniel Alonso. "Semiclassical quantization and classical chaotic systems." Doctoral thesis, Universite Libre de Bruxelles, 1995. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/212531.

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38

Richardson, Julie K. "Parametric modelling for linear system identification and chaotic system noise reduction." Thesis, University of Strathclyde, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.405388.

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39

Rosenblum, Michael G. "Phase synchronization of chaotic systems from theory to experimental applications /." [S.l. : s.n.], 2002. http://pub.ub.uni-potsdam.de/2003/0007/rosenbl.pdf.

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40

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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41

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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42

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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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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44

Locquet, Alexandre Daniel. "Chaotic optical communications using delayed feedback systems." Diss., Georgia Institute of Technology, 2006. http://hdl.handle.net/1853/10431.

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Chaotic dynamics produced by optical delay systems have interesting applications in telecommunications. Optical chaos can be used to transmit secretly, in real-time, a message between an emitter and a receiver. The noise-like appearance of chaos is used to conceal the message, and the synchronization of the receiver with the chaotic emitter is used to decode the message. This work focuses on the study of two crucial topics in the field of chaotic optical communications. The first topic is the synchronization of chaotic external-cavity laser diodes, which are among the most promising chaotic emitters for secure communications. It is shown that, for edge-emitting lasers, two drastically different synchronization regimes are possible. The regimes differ in terms of the delay time in the synchronization and in terms of the robustness of the synchronization with respect to parameter mismatches between the emitter and the receiver. In vertical-cavity surface-emitting lasers, the two linearly-polarized components of the electric field also exhibit isochronous and anticipating synchronization when the coupling between the lasers is isotropic. When the coupling is polarized, the linearly-polarized component that is parallel to the injected polarization tends to synchronize isochronously with the injected optical field, while the other component tends to be suppressed, but it can also be antisynchronized. The second topic is the analysis of time series produced by optical chaotic emitters subjected to a delayed feedback. First, we verify with experimental data that chaos produced by optical delay systems is highly complex. This high complexity is demonstrated by estimating chaos dimension and entropy from experimental time series and from models of optical delay systems. Second, by analyzing chaotic time series, it is shown that the value of the delay of a single-delay system can always be identified, independently of the type of system used and of its complexity. Unfortunately, an eavesdropper can use this information on the delay value to break the cryptosystem. We propose a new cryptosystem with two delayed feedback loops that increases the difficulty of the delay identification problem.

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45

Kim, Ho Jun. "Quantification of chaotic mixing in microfluidic systems." Texas A&M University, 2004. http://hdl.handle.net/1969.1/1084.

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Periodic and chaotic dynamical systems follow deterministic equations such as Newton's laws of motion. To distinguish the difference between two systems, the initial conditions have an important role. Chaotic behaviors or dynamics are characterized by sensitivity to initial conditions. Mathematically, a chaotic system is defined as a system very sensitive to initial conditions. A small difference in initial conditions causes unpredictability in the final outcome. If error is measured from the initial state, the relative error grows exponentially. Prediction becomes impossible and finally, chaotic systems can come to become stochastic system. To make chaotic motion, the number of variables in the system should be above three and there should be non-linear terms coupling several of the variables in the equation of motion. Phase space is defined as the space spanned by the coordinate and velocity vectors. In our case, mixing zone is phase space. With the above characteristics - the initial condition sensitivity of a chaotic system, our plan is to find most efficient chaotic stirrer. In this thesis, we present four methods to measure mixing state based on the chaotic dynamics theory. The Lyapunov exponent is a measure of the sensitivity to initial conditions and can be used to calculate chaotic strength. We can decide the chaotic state with one real number and measure efficiency of the chaotic mixer and find the optimum frequency. The Poincare section method provides a means for viewing the phase space diagram so that the motion is observed periodically. To do this, the trajectory is sectioned at regular intervals. With the Poincare section method, we can find 'islands' considered as bad mixed zones so that the mixing state can be measured qualitatively. With the chaotic dynamics theory, the initial length of the interface can grow exponentially in a chaotic system. We will show the above characteristics of the chaotic system to prove as fact that our model is an efficient chaotic mixer. The final goal for making chaotic stirrer is how to implement efficient dispersed particles. The box counting method is focused on measurement of the particles dispersing state. We use snap shots of the mixing process and with these snap shots, we devise a plan to measure particles' dispersing rate using the box-counting method.

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Lesnik, Dmitry. "Transport scaling in incompletely chaotic Hamiltonian systems." [S.l.] : [s.n.], 2002. http://deposit.ddb.de/cgi-bin/dokserv?idn=964989263.

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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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Everson, R. M. "Detection and description of deterministic chaotic systems." Thesis, University of Leeds, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.233210.

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Yannacopoulos, A. N. "Diffusion models in strongly chaotic Hamiltonian systems." Thesis, University of Warwick, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.357654.

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Shin, Kihong. "Characterisation and identification of chaotic dynamical systems." Thesis, University of Southampton, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.242459.

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