Control Of Spatiotemporal Chaos In Coupled Map Lattices

Chaos exists and acts an important role in many engineering application and scientific research, so it becomes more and more important to control chaos. Although studies on the control of chaos have made a rapid progress since 1990s, the exploration on the methods of control chaos still stay at the early stage and there are a large number of problems remain to be resolved. In this dissertation, the studies are carried out mainly on the controlling problems of spatiotemporal chaos in coupled map lattices.In Chapter one we introduce briefly the history and current developments of the spatiotemporal chaos in coupled map lattices. Then we focus on the investigation history and current situations of chaos control in the past ten years. Chapter two introduces the main knowledge of chaos and chaos control. In chapter three, we briefly introduce the spatiotemporal chaos and six spatiotemporal behaviors in coupled map lattices. In chapter four, We introduce two new feedback control methods, linear feedback control method and non-linear feedback control method. Using these two methods to control the Pattern Selection and Pattern Competition Intermittency, we can get good controlling results. What's more, we can convert all state variables of the model system to a fixed point or a series of steady points(these steady points are certain values). The numerical simulation results demonstrate that this method is effective. From the numerical simulation results, these two control methods are very flexible. Using different feedback control methods and different control parameters, we can get different control goals. Compared to other methods of feedback control, these two methods can achieve stable state with less iteration steps and more simple calculation process. This is very useful in practical application.Finally, in chapter five and six, we summarize the whole dissertation and the further research in the future.