The Nonlinear Dynamics Of Coupling Arrays And The Application To Secure Communication

The field of dynamical systems and especially the study of chaotic systems has been considered as one of the important breakthroughs in science in this century. While this area is still relatively young, there is no question that it is becoming more and more important in a variety of scientific disciplines. Thus, this work starts with an historical overview about nonlinear dynamics and chaotic behavior that introduces the application to the secure communication field which is presented in the subsequent chapters. Research work of this dissertation has two main parts as follows:One part of the present thesis is devoted to show different categories of connections among chaotic systems that can lead to rich dynamical behaviors, especially chaotic synchronization. For open linear geometries (Chain), the chaotic cells are seen to synchronize consecutively as a synchronization wave spread through the arrays. For circular loops (Ring), it is found that there is a critical number of cells above which the uniform synchronized state is not stable and exhibits chaotic rotating waves or periodic rotating waves. For the coupled ring and linear arrays, it is found that the chaotic rotating waves generated from the ring propagate with spatial periodic synchronization along the Chain, that is to say ,two chaotic oscillators in the Chain are synchronization if the number of oscillators(spatial distance)between them is a multiple of oscillator number in the ring. Numerically it is shown that the stabilities of the synchronization states are enhanced by chaos, and degraded when the oscillators are far from the ring.The other part of the present thesis deals with possible applications of chaotic systems to the communications field. Based on the spatial periodic chaos synchronization in coupled ring and linear arrays, we proposed a random high-dimensional chaotic encryption scheme. The transmitter can choose hyperchaoticsignals randomly from the ring at any different time and simultaneously transmit the information of chaotic oscillators in the ring to receiver through public channel, so that the message can be masked by different hyperchaotic signals in different time intervals during communication, and the receiver cannot decode the message. Furthermore, the high sensitivity to the symmetry of the coupling structure makes the attacker very difficult to obtain any useful message from the channel which greatly enhanced the scheme's security. This work has been published in Phys. Lett. A335(2-3), 191-196(2005).