Thesis (M.A.)--Harding University Graduate School of Religion, 2002. / Committee chair Professor Phillip McMillion. Includes bibliographical references (leaves 191-209).

Thesis (M.A.)--Abilene Christian University, 2002. / Includes abstract. Includes bibliographical references (leaves 95-102).

Thesis (M.A.)--Abilene Christian University, 2002. / Includes abstract. Includes bibliographical references (leaves 95-102).

Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 98-102). Available also in a digital version from Dissertation Abstracts.

Thesis (M.A.)--Abilene Christian University, 2002. / Includes abstract. Includes bibliographical references (leaves 95-102).

Synchronization of chaos in coupled systems of ordinary differential equations is an area of mathematics which has attracted much attention in recent years, in particular for the potential technological applications such systems have in engineering and industry. The motivation for this research was to understand mathematically, synchronization observed in systems of two and three solid state lasers studied by collaborators at the Georgia Institute of Technology. The main objectives of this thesis are to understand more clearly some of the dynamical phenomena associated with the synchronization of chaos, and to develop new techniques for the analysis of dynamical systems with symmetry; with a view to applying these techniques to models of solid state laser systems and other applications. First we introduce the main ideas of chaotic synchronization and some useful tools for the analysis of dynamical systems with symmetry. We then introduce a model for a solid state Nd:YAG laser and examine the types of dynamics which may be exhibited. Subsequently we look at systems of two and three coupled solid state lasers and examine the onset of synchronization in such systems, both in a fully symmetric system and in the case of two coupled lasers, the case of broken symmetry. We then contrast these results with those of a modified Rossler system and observe similar results in both cases. We examine how chaotic systems may be used for communication purposes and develop a new scheme for the communication of a signal using the synchronization of chaos. Finally we introduce a new definition of attractor and using topological and measure theoretic properties of sets, we reexamine the concepts of basin riddling and are able in certain situations to determine the presence or otherwise of riddling.

No description available.

The nonlinear dynamics of three physical systems has been investigated. Diode resonator systems are experimentally shown to display a period doubling route to chaos, quasiperiodic states, periodic locking states, and Hopf bifurcation to chaos. Particularly, the transition from quasiperiodic states to chaos in line-coupled systems agrees well with the Curry-Yorke model. The SPICE program has been modified to give realistic models for the diode resonator systems.

Verteilte Softwaresysteme bringen ein sehr komplexes Verhalten unter echten Einsatzbedingungen mit sich, meist resultiert dies auch in sehr komplexen Fehlerzuständen, die durch den Betrieb unter widrigen Netzwerkbedingungen wie beispielsweise hohen Latenzen und zunehmenden Paketverlusten entstehen. Diese Fehlerzustände können mit herkömmlichen Softwaretestverfahren wie Unit- und Integrationstests nicht mehr hinreichend provoziert, getestet und verifiziert werden. Mit der Methode des Chaos-Engineerings werden komplexe Chaos-Szenarien entworfen, die es ermöglichen dieses unbekannte Verhalten der Software in Grenzfällen strukturiert zu entdecken. Am Beispiel einer verteilten Software, die bereits seit über 10 Jahren am Deutschen Zentrum für Luft- und Raumfahrt (DLR) entwickelt wird, werden Chaos-Engineering-Methoden angewandt und sowohl konzeptuell in existierende Softwaretestverfahren eingeordnet als auch praktisch in einer Experimental-Cloud-Umgebung erprobt. Innerhalb eines Experteninterviews mit den RCE-Entwicklern wird ein Chaos-Szenario entworfen, in der die Robustheit der Software mit Chaos-Experimenten auf die Probe gestellt wird. Aufbauend auf einem Softwareprojekt zur automatischen Erstellung von RCE-Testnetzwerken, wird eine Softwarelösung entwickelt, die eine automatische Ausführung von Chaos-Szenarien innerhalb der Experimental-Cloud-Umgebung ermöglicht. Anschließend wird das aus den Experteninterviews resultierende Chaos-Szenario in der Praxis durchgeführt. Abschließend werden die Erkenntnisse aus der Ausführung des Chaos- Szenarios vorgestellt und weiterführende Fragestellungen und Arbeiten aufgezeigt:1 Einleitung 2 Grundlagen 2.1 Softwareentwicklung und Testverfahren 2.2 Verteilte Software 2.3 Containerorchestrierung 2.4 Chaos Engineering 3 Betrachtetes System 3.1 Remote Component Environment 3.2 Testing von RCE Releases 3.3 Methode Experteninterview 3.4 Fragestellungen entwerfen 3.5 Resultate aus Interview 3.6 Integration von Chaos-Engineering 4 Konzepte des Chaos-Engineering am Beispiel 4.1 Ausgangssituation 4.1.1 Systemumgebung 4.1.2 Automatisierte Erstellung von Testnetzwerken 4.1.3 Microservices 4.1.4 Systemarchitektur 4.1.5 Netzwerkbeschreibung 4.2 Anforderungen an die zu entwickelnde Software 4.3 Erweiterung des vorhandenen Gesamtsystems 4.3.1 Chaos Mesh 4.4 Chaos-Operator Microservice 4.4.1 Erweiterung der Systemarchitektur 4.4.2 Erweiterung der Schnittstellen 4.4.3 Beschreibung eines Chaos-Experiments 4.4.4 Probes 4.4.5 Ablaufsteuerung 5 Evaluierung und Diskussion 5.1 Geplantes Chaos-Szenario 5.1.1 JSON Beschreibung eines Chaos-Szenarios 5.2 Durchführung des entworfenen Chaos-Szenarios 5.2.1 Ausführung mit Chaos-Sequencer 5.2.2 Validierung 5.3 Resultate 6 Fazit Literaturverzeichnis Abbildungsverzeichnis Listings

Chaos theory is well known as one of three revolutions in physical sciences in 20th-century, as one physicist called it: Relativity eliminated the Newtonian illusion of absolute space and time; quantum theory eliminated the Newtonian dream of a controllable measurable process; and chaos eliminates the Laplacian fantasy of deterministic predictability". Specially, when chaos synchronization was found in 1991, chaos theory becomes more and more attractive. Chaos has been widely applied to many scientific disciplines: mathematics, programming, microbiology, biology, computer science, economics, engineering, finance, philosophy, physics, politics, population dynamics, psychology, and robotics. One of most important engineering applications is secure communication because of the properties of random behaviours and sensitivity to initial conditions of chaos systems. Noise-like dynamical behaviours can be used to mask the original information in symmetric cryptography. Sensitivity to initial conditions and unpredictability make chaotic systems very suitable to construct one-way function in public-key cryptography. In chaos-based secure communication schemes, information signals are masked or modulated (encrypted) by chaotic signals at the transmitter and the resulting encrypted signals are sent to the corresponding receiver across a public channel (unsafe channel). Perfect chaos synchronization is usually expected to recover the original information signals. In other words, the recovery of the information signals requires the receiver's own copy of the chaotic signals which are synchronized with the transmitter ones. Thus, chaos synchronization is the key technique throughout this whole process. Due to the difficulties of generating and synchronizing chaotic systems and the limit of digital computer precision, there exist many challenges in chaos-based secure communication. In this thesis, we try to solve chaos generation and chaos synchronization problems. Starting from designing chaotic and hyperchaotic system by first-order delay differential equation, we present a family of novel cell attractors with multiple positive Lyapunov exponents. Compared with previously reported hyperchaos systems with complex mathematic structure (more than 3 dimensions), our system is relatively simple while its dynamical behaviours are very complicated. We present a systemic parameter control method to adjust the number of positive Lyapunov exponents, which is an index of chaos degree. Furthermore, we develop a delay feedback controller and apply it to Chen system to generate multi-scroll attractors. It can be generalized to Chua system, Lorenz system, Jerk equation, etc. Since chaos synchronization is the critical technique in chaos-based secure communication, we present corresponding impulsive synchronization criteria to guarantee that the receiver can generate the same chaotic signals at the receiver when time delay and uncertainty emerge in the transmission process. Aiming at the weakness of general impulsive synchronization scheme, i.e., there always exists an upper boundary to limit impulsive intervals during the synchronization process, we design a novel synchronization scheme, intermittent impulsive synchronization scheme (IISS). IISS can not only be flexibly applied to the scenario where the control window is restricted but also improve the security of chaos-based secure communication via reducing the control window width and decreasing the redundancy of synchronization signals. Finally, we propose chaos-based public-key cryptography algorithms which can be used to encrypt synchronization signals and guarantee their security across the public channel.