Control And Synchronizing Spatiotemporal Chaos

In the last half of twentieth century, chaos has been thoroughly investigated and well understood in many aspects, and become the central field in nonlinear science. Now, chaos application appears to be one of the most important tasks for further developing of the field. In this respect, chaos control and synchronization are topics of most relevance. Rather recently, a great interest of chaos control and synchronization has been shifted to spatiotemporal systems. On one hand, turbulence and turbulence control remain among the extremely important problems in nature science for more than one century, and chaos control in spatiotempral systems is directly aiming at the goal of turbulence control;on the other hand, each chaotic spatiotemporal system is a reservoir of rich patterns (incomparably richer than nonchaotic systems), and the utilization of these patterns has a great potential of applications in wide fields. In this thesis, we will focus on the study of chaos and turbulence control and synchronization and controllable pattern formations in spatiotemporal systems. And the application of spatiotemporal chaos synchronization in secure communications will be also considered.The first chapter is an introduction. In this chapter, some background about chaos and chaos control and synchronization is summarized.The second chapter contains two parts. First, size-induced instabilities in one-dimensional complex Ginzburg-Landau equation (CGLE) is numerically investigated in detail. We show how the system dynamics is varied from periodicity to fully-developed turbulence by increasing its size only. Second, pattern and turbulence control is studied in CGLE. It is shown that in fully-developed turbulence region (when a large number of positive Lyapunov exponents exist), and in the presence of large gradient force, we can drive the systems to various wanted spatiotemporal patterns, and control and synchronize violent turbulence by applying convenient local pinning and boundary control techniques.The third chapter is devoted to spiral waves control. Spiral waves of excitation belong to the most intriguing spatiotemporal patterns in nonequilibrium reaction-diffusion systems. We take two-dimensional coupled Chua's circuits in excitable and oscillatory media and two-dimensional reaction diffusion equations in excitable medium as our models. In certain parameter regions above spatiotemporal systems have both spiral wave state and some homogeneous states. Feedback pinnings are suggested to migrate the system from the spiral wave to various wanted patterns. The influences of pinning density, forcing strength, and different pinning distributions on the driving effect are investigated. It is shown that some properly designed control schemes may reach very high control efficiency, and we realize annihilating spiral waves by using very few pinning cells only.In the fourth chapter, we propose a new chaotic secure communication system: multi-channel spread-spectrum communication system based on spatiotemporal chaos synchronization. First, for achieving high efficiency of spatiotemporal chaotic synchronization, we take one-way coupled map lattices(OCML) as our model, and find that two identical OCML can be synchronized by using a single driving key;Second, like conventional spread-spectrum techniques, our approach is based on correlation technique, so large number of informative signals carried by different chaotic sequences can be transmitted by using a single signal sequence and received simultaneously;Third, due to the fact our chaotic sequences are high-dimensional hyperchaos, there are more robust and safe against external imitations and attacks than that of synchronizing low-dimensional chaos. The proposed systems are performed successfully by computer simulation, the error probability is nearly the same as Gold sequences which are used in modern spread-spectrum communication systems.