Synchronizing multiple-dimensional chaotic systems and using them in communication

Synchronizing Multiple-Dimensional Chaotic Systems and Using Them in Communication In general, most of natural phenomenon looks like the dynamic behavior of nonlinear systems. Although it is easy to predict the behavior of linear systems, to predict that of nonlinear systems becomes rather diffucult, especially where it exibits chaos. In this work, first an introduction to linear and nonlinear system characteristics, the concepts stability and divergence are discussed in detail. Some known routes by which a nonlinear system can proceed to chaos are introduced, and to further illuminate the routes an outline of some additional system analysis methods such as Lyapunov spectrum, Kolmogorov entropy, Lyapunov and fractal dimensions, time series, Poincare maps, and power spectrum are presented. After, the behavior of chaotic Van der Pol-Duffing oscillators (VPDO), selected as a sample chaotic dynamic system is investigated using known chaotic analysis methods, and then applied to the communication field to achieve more secure communi cation. Since such communication requires synchronization of transmitter with receiver the method proposed by Pecora and Carroll for synchronizing Rössler and Lorenz systems is applied to the 3-dimensional VPDO. To allow the transmission of more than one information at the same time, the dimension of the system used is increased to produce several driving signal, each of which is for one information. So, the drive system is divided into several subsystems to increase the dimension up to 4, 5, 6, 7, or 8, and the synchronization results are verified by the computer simulation. In addition, derived is a robust relationship between system dimension and Kolmogorov entropy. In multi dimensional VPDO systems made apropriate Lyapunov functions have been found to establish the stabilization of response subsystems of the systems used in the case where there are one or more driving varibles. Finally, it has been shown that synchronization between 3-dimensional Lorenz and VPDO systems are achieved using single state variable. Key Words: Chaos, Strange Attractor, Lyapunov Exponents, Lyapunov and Fractal Dimension, Period-Doubling, Poincare Map, Entropy, Kolmogorov Entropy, Master System, Drive Subsystem, Slave Subsystem. VI