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.

Complex oscillations including chaotic motions have been identified in off-shore and submerged mooring systems characterized by nonlinear fluid-structure interactions and restoring forces. In this paper, a means of controlling these nonlinear oscillations is addressed. When applied, the controller is able to drive the system to periodic oscillations of arbitrary periodicity. The controller applies a perturbation to the nonlinear system at prescribed time intervals to guide a trajectory towards a stable, periodic oscillatory state. The controller utilizes the pole placement method, a state feedback rule designed to render the system asymptotically stable. An outline of the proposed method is presented and applied to the fluid-structure interaction system and several examples of the controlled system are given. The effects of random noise in the excitation force are also investigated and the subsequent influence on the controller identified. A means of extending the controller design is explored to provide adequate control in the presence of moderate noise levels. Meanwhile, in the presence of over powering noise or system measurements that are not well defined, certain filtering and estimation techniques are investigated for their applicability. In particular, the Iterated Kalman Filter is investigated as a nonlinear state estimator of the nonlinear oscillations in these off-shore compliant structures. It is seen that although the inclusion of the nonlinearities is theoretically problematic, in practice, by applying the estimator in a judicious manner and then implementing the linear controllers outlined above, the system is able to estimate and control the nonlinear systems over a wide area of pseudo-stochastic regimes. / Graduation date: 2006

Chaotic dynamics are at the center of multiple studies to perfect encrypted communication systems. Indeed, the particular time evolution nature of chaotic signals constitutes the fundamentals of their application to secure telecommunications. The pseudo random signal constitutes the carrier wave for the communication. The information coded on the carrier wave can be extracted with knowledge of the system dynamic evolution law. This evolution law consists of a second-order delay differential equation in which intervene the various parameters of the physical system setup. The set of precise parameter values forms the key, in a cryptographic sense, of the encrypted transmission. This thesis work presents the implementation of an experimental encryption system using chaos. The optical intensity of the emitter fluctuates chaotically and serves as carrier wave. A message of small amplitude, hidden inside the fluctuations of the carrier wave, is extracted from the transmitted signal by a properly tuned receiver. The influence of the message modulation format on the communication quality both in the back to back case and after propagation is investigated numerically.

M. Tech. Electrical engineering. / Discusses a desirable chaos-based encryption scheme for image storage and transmission is one that can resist different types of attacks in less time and with successful decryption. To resist different kinds of attacks, a higher security level is required. As a result, there is a need to enhance the security level of existing chaos-based image encryption schemes using hyper-chaos. To increase the level of security using hyper-chaos, the research will present a scheme that combines two different techniques that are used to improve the degree of security of chaos-based cryptography; a classical chaos-based cryptographic technique and a hyper-chaos masking technique. The first technique focuses on the efficient combination and transformation of image characteristics based on hyper-chaos pseudorandom numbers. The second technique focuses on driving the hyper-chaos system by using the results of the first technique to change the transmitted chaos dynamic as well as using synchronisation and a high-order differentiator for decryption. To achieve the objective of our research the following sub-problems are addressed.

published_or_final_version / abstract / Electrical and Electronic Engineering / Master / Master of Philosophy

The first part of this work deals with open dynamical systems. A natural question of how the survival probability depends upon a position of a hole was seemingly never addresses in the theory of open dynamical systems. We found that this dependency could be very essential. The main results are related to the holes with equal sizes (measure) in the phase space of strongly chaotic maps. Take in each hole a periodic point of minimal period. Then the faster escape occurs through the hole where this minimal period assumes its maximal value. The results are valid for all finite times (starting with the minimal period), which is unusual in dynamical systems theory where typically statements are asymptotic when time tends to infinity. It seems obvious that the bigger the hole is the bigger is the escape through that hole. Our results demonstrate that generally it is not true, and that specific features of the dynamics may play a role comparable to the size of the hole. In the second part we consider some classes of cellular automata called Deterministic Walks in Random Environments on Z^1. At first we deal with the system with constant rigidity and Markovian distribution of scatterers on Z^1. It is shown that these systems have essentially the same properties as DWRE on Z^1 with constant rigidity and independently distributed scatterers. Lastly, we consider a system with non-constant rigidity (so called process of aging) and independent distribution of scatterers. Asymptotic laws for the dynamics of perturbations propagating in such environments with aging are obtained.

Thesis (Ph.D.)--McMaster University (Canada), 1996. / Source: Dissertation Abstracts International, Volume: 57-10, Section: B, page: 6457. Adviser: S. Haykin.

Thesis (Ph.D.) -- University of Newcastle, 2002. / Faculty of Education. Includes bibliographical references (leaves 194-222). Also available online.

Thesis (Ph. D.)--University of Washington, 1995. / Vita. Includes bibliographical references (leaves [75]-79).

Thesis (Ph. D.)--University of Hong Kong, 2008. / Includes bibliographical references (p. 169-182) Also available in print.