Title of Dissertation: Application of Chaotic Synchronization and Controlling Chaos to Communications Application of Chaotic Synchronization and Controlling Chaos to Communications

Title of Dissertation: Application of Chaotic Synchronization and Controlling Chaos to Communications Vasily Dronov, Doctor of Philosophy, 2005 Dissertation directed by: Professor Edward Ott Department of Electrical and Computer Engineering This thesis addresses two important issues that are applicable to chaotic communication systems: synchronization of chaos and controlling chaos. Synchronization of chaos is a naturally occurring phenomenon where one chaotic dynamical system mimics dynamical behavior of another chaotic system. This phenomenon can be used in chaotic communication system as a mechanism for information decoding whereas controlling chaos can be used to encode information into the dynamics of the system. Apart from this particular application, the phenomenon of chaotic synchronization is a popular topic of research, in general, and has attracted much attention within the scientific community. Controlling chaos is another potential engineering application. A unique property of controlling chaos is the ability to cause large long-term impact on the dynamics using arbitrarily small perturbations. This thesis is broken up into three chapters. The first chapter contains a brief introduction to the areas of research of the thesis work, as well as the summaries the work itself. The second chapter is dedicated to the study of a particular situation of chaotic synchronization which leads to a novel structure of the basin of attraction. This chapter also develops theoretical scalings applicable to these systems and compares results of our numerical simulations on three different chaotic systems (two discrete maps and one continuous flow) with theoretical results. The third chapter consists or two logically connected parts (as both of them study chaotic dynamics of systems that can be modeled with delayed differential equations). The first and the main part presents a study of a chaotically behaving traveling wave tube, or TWT, with the objective of improving efficiency of satellite communication systems. In this work we go through an almost complete design cycle, where, given an objective, we begin with developing a nonlinear model for a generic TWT; we then study numerically the dynamics of the proposed model; we find conditions where chaotic behavior occurs (we argue that TWT in chaotic mode could be more power efficient); then we use the idea of controlling chaos for information encoding; we support the concept with numerical simulations; and finally analyze the performance of the proposed chaotic communication system. The second part of this chapter describes an experiment with a pair of electronic circuits modeling the well-known Mackey-Glass equation. Despite the simplicity of the circuits, they represent a powerful experimental tool, as they are capable of exhibiting various types of dynamic behavior (fixed point, limit cycle, chaos including high-dimensional chaos with Lyapunov dimension >10). A simple experiment where human voice was encoded into chaotic signal had been conducted which showed a possibility of engineering application of chaos to secure communications.