The Synchronization Study Of Improved Hyperchaotic Lü System

This thesis primarily focuses on the synchronization problem of improved hyperchaotic Lüsystem. On the basis of theoretical analysis, it makes in-depth research in this field. My work includes numerical calculations, circuit simulations, circuit experiments as well as demonstration in all results.Firstly, it introduces the situations of the developments of chaotic theory and the current status of the study of chaotic synchronization. Meanwhile, confirming the significance and purpose of this research.Secondly, it shows dynamics features of the hyperchaotic Lüsystem by the means of numerical simulation which reveal complexity of its chaotic behavior. In order to translate mathematical model of this system into physical model, we need to do scale conversion, then get state equations and work out electric schematic diagram. Furthermore, we gain the experimental results and numerical value, which correspond with the results of circuit simulation that putting to use Pspice via circuit experiments.Thirdly, it discusses in detail about self-synchronizing problem of improved hyperchaotic Lüsystem which mainly adopt linearity feedback method, nonlinearity feedback method, active control method, state observer method, adaptive method and so on. At this stage, we design the appropriate controller separately in response to synchronization of system and driving system. Then go into numerical simulation and find the synchronization effect of these synchronization methods from error chart definitely. If the experimental results and numerical value coincide with circuit simulation, it will demonstrate validity of controller.Finally, it comes into the stage of synchronization problem among different systems through nonlinearity feedback method, active control method and adaptive method. Our purpose is to realize different structure synchronization of improved hyperchaotic Lüsystem and hyperchaotic Lorenz system. Simulations and experimental results are used to test feasibility and validity of synchronization methods.Above all, this paper is going to put improved hyperchaotic Lüsystem into practice. It offers vita theoretical analysis and experimental evidences, and maybe this work is a little helpful for other synchronization researches of chaos systems.