Chaos Control And Generalized Synchronization In Electric-optical Bistable Systems

In this paper,based on characteristics of the electro-optical bistable systems under the condition of the long delay, we study the dynamics of the system. chaos control and synchronization in detail. The main contents of the full text include the following:The first chapter summarizes the development of chaotic dynamics; the status quo of the optical bistable system ; then we give the contents and concrete structure of this paper .The second chapter introduces the basic concepts of chaos, reviewes the characteristics of the chaotic ways and means.The third chapter proposes methods of the theory combined with the latest developments in research on chaos control and synchronization.The forth chapter investigates properties of the dynamics , chaos control and generalized chaos synchronization of the long delayed electro-optical bistable systems. They are the main parts of the thesis.In the electro-optical bistable systems dynamics research, based on the time evolution equation of the long delayed electro-optical bistable systems .we have analysized in detail the process of the system after entering the chaotic period-doubling bifurcation. We found with the bifurcation parameters - a light intensity increasing, the system will go through the state of the process of period-doubling bifurcation from the steady-state into a state of chaos. From numberical calculation we can see that: With the strong increase of the light intensity, the system experienced a number of period-doubling bifurcation process. Each bifurcation begins with the process that is used to directly jump to the chaotic state of cycle 1, and from which to the next process of period-doubling bifurcation. Overall, with the bifurcation speed faster and faster ,pace cycle becomes more and more smaller regions, however,the chaotic region becomes larger and larger. At the same time, The window effect of chaotic region is not obvious. This phenomenon is the first time we found. The results of research on the electro-optical bistable systems provides the necessary theoretical basis for the practical application.On chaos control and synchronization, we can use two methods: chaotic signal and chaotic signal driven modulation parameters to study chaotic control and generalized chaos synchronization of the electro-optical bistable systems. S1 is the driving system and S2, and are two identical driven systems. We make the output from S1 summing to the output from S2 and S3 respectively to drive the two driven systems S2 and S3 in order to achieve a dynamic drive..Based on the above program, by numerical calculation, we studied the conditions and rules of chaotic driven system for control and generalized chaos synchronization between driving system and driven systems.On chaos control of driven systems, driving systems that drives the state or intensity modulation control of the outcome of driven system is decisive. When the driving system in a state cycle, with the driving intensity increases gradually from small to big, the driven system state will change and control a wide range of cycle status.The control of chaotic systems mainly go through two ways: the one way is that the system control to chaos with periodic windows of the various cycles and the ensuing evolution of the state into chaos once again . When driving intensity reach a certain value , the systems go into the state of cycle 1 and after a period-doubling bifurcation enter into a different cycle t state. Another way the system through a down period-doubling bifurcation process is controlled into a wide range of cycle status. The results from the control point of view, the first means of a control system can control the state of all cycles. The other way that controls the minimum cycle status is the same to state of driven system.And the parameters for the chaotic signal modulation, chaos systems control have also gone through the two processes: One is that the system enters into the cycle window through the chaotic state and then achieve a stable state of a wide range of cycle control; second, first making chaotic systems entering into cycle window to make it into the multi-cycle status, and then jump to another cycle bifurcation region after the process of being entered into a wide variety of cycle status. In the driving system and driven system of generalized chaos synchronization, we studied the main driving and driven system in the same or a different state of generalized chaos synchronization.On the generalized synchronization of the driving systems and driven systems. We mainly analyse generalized synchronization in the same or different condition of chaotic state.Though deducing the Maximal Conditional Lyapunov exponent of the driven systems, above all, we analyse the parameters. condition that driving and driven systems achieve synchronization.From calculating the Maximal Conditional Lyapunov exponent of the driven systems by using chaotic signal and chaotic signal modulation parameters, we can see that with the increase of the driving stiffness or modulation stiffness q ,the driven system have a range of less than zero. This shows that driven systems and driving systems can achieve a generalized chaos synchronization in the range. Thus, we have confirmed the range of parameters that the driven systems and driving systems achieve chaos synchronization .To further explain the generalized synchronization of the driving systems and driven systems, we also have studied the timing chart between the driving systems and driven systems. From numberical calculation we can see that only by meeting the conditions, the driving systems and driven systems can achieve generalized synchronization.In essence, the above two methods belonged to the unilateralism driveing, and we have received very resembled result on studying the chaos control and synchronization of electro-optical bistable systems. Difference is:that as the parameters and state parameters of the system, the role is different, so specific details are different.The largest characteristic of our project is that by using the same program. you can adjust the system status and driving parameters, namely realized the chaos control and generalized synchronization, which have in practice is an important value in practice .