Study On The Control Of Spatiotemporal Chaos

Spatiotemporal chaos exists in a variety of nonlinear systems such as fluid dynamics system, plasma system, optical system, and reaction-diffusion system. Chaotic behaviors of the actual situation are generally considered to be harmful. For instance, flow turbulence enhances energy consumption of ships, pipelines, automobiles, and aircrafts,the breakup of spiral wave in cardiac tissues can lead to ventricular fibrillation, and so on. Therefore, the control of spatiotemporal chaos is very important for elimination of chaos harm.Turbulence is very universal phenomenon in nature and projects. After long term research of flow turbulence, one found that there is large-scale structure (i.e., coherent structure) in chaotic flow, i.e., flow turbulence is composed of different scale vortex. The pattern of turbulence is determined by the vortex structure. We must grasp the motion law of flow turbulence through the motion of vortex mode. However, the investigations about vortex focus only on the merger, control, coupled polarization and motion of vortex so far. The influences of the interaction between modes on dynamical behavior of flow turbulence and the merger of vortex have not been studied by scientists. This study is important for understanding of the physical nature of flow turbulence and grasping the role of different vortex in process of the merger, evolution and control of vortex.It is generally believed that the control of flow turbulence could benefit from those strategies developed in controlling chaotic systems. So far, spatiotemporal chaos has been investigated extensively. However, controlling flow turbulence based on the applications of spatiotemporal chaos control methods (i.e., the method of directly operating flow field) is just at its beginning. Recently, the local and global pinning control methods developed in spatiotemporal chaos control have been applied to control two-dimensional turbulence described by incompressible Navier-Stokes equation (NS equation). It is shown that the turbulence can be controlled to desirable time-varying target states. But the methods have a shortcoming since they are only suitable for special target state. How to propose more effective control method of flow turbulence need further investigation. In this paper, we investigate the interaction network of vortex mode in flow turbulence. The control methods of the 2D turbulence and instable spiral wave are proposed. The results are introduced as follows.In chapter 1, the chaotic phenomena, chaos control methods, flow turbulence, and the generation and control of spiral wave are briefly introduced.In chapter 2, the flow turbulence described by two-dimensional Navier-Stokes is composed of many vortex modes, which can be divided into four types of modes. The interactions between modes are studied based on the four types of modes. A method of constructing network is proposed. The interaction network for one type of modes is built. It is shown that the network has the feature of scale-free network. The evolution of two-dimensional turbulence is analyzed, based on the interaction network of vortex mode.In chapter 3, the control of flow turbulence described by two-dimensional Navier-Stokes equation is considered. The space-shift feedback method is proposed. It is found that flow turbulence can be controlled to a regular state when control parameters are suitably chosen. Flow turbulence can be controlled to laminar flow if using unidirectional space-shift feedback,whereas flow turbulence can be controlled to regularly vortex states with different sizes of vortices if using bidirectional space-shift feedback. The controlled vortex does not move when special control parameters are applied. The physical mechanism is briefly analyzed, based on space correlation.In chapter 4, the control of unstable spiral wave described B?r model is considered. In order to prevent the breakup of unstable spiral wave, we apply space force to prevent the system to return to the rest state. It is found that the unstable spiral wave (the parameters of the system are in turbulent region) can be controlled to stable spiral wave by the space force when control parameters are suitably chosen. Comparing the excitation frequency of medium without space force with the excitation frequency of medium without space force, we find that the space force effectively enhance the excitation frequency of medium so that the unstable spiral wave become stable spiral wave due to the increase of the frequency of the spiral wave. The breakup of spiral waves is prevented by the space force.