Synchronization Research Of Several Typical Chaotic Systems

There are more or less non-linear characteristic in all of the application systems. Some of them are inherent, while others need to use the non-linear characteristic of the electronic devices to meet the non-linear requirements. Therefore, it's very important to analysis the characteristics of the non-linear system and to research the controlling methods of it. In this paper, using a combination method of theoretical proof and numerical analysis, I do the research as follow:The synchronization problem of chaotic and hyper-chaotic systems is discussed using the active control method and the state feedback method. And based on the Lyapunov stability theory, the sufficient conditions on the system synchronization are given. Numerical simulation further confirms the validity of the method.The adaptive controller of the hyper-chaotic system is designed based on the adaptive synchronization method. This controller is not only effective to the hyper-chaotic systems with the same structure, but also effective to the diverse hyper-chaotic systems, even the systems with unknown parameters. Therefore, this method expands the range of applications of chaos synchronization in practice.The dynamic behavior of a new kind unified hyper-chaotic system is researched. The unified hyper-chaotic system is analysised based on the coupled synchronization methods, and the synchronization criterion of two coupled unified hyper-chaotic systems is given.Based on the dual synchronization theory, the synchronization problem of unified chaotic system is researched, and the dual synchronization state is defined, and the design criterion of the dual synchronization controller is given. The synchronization is realized. The simulation results show that this scheme can not only be used to the chaotic system with the same structure, but also can be used to the diverse chaotic systems.Based on the stability theory of fractional order systems, with active control technology, the diverse synchronization conditions of the fractional order hyper-chaotic Lorenz systems and the fractional order hyper-chaotic Rossler is analysed. And the paper takes the base order 0.97 for examples, gives the numerical simulation. And the simulation result verified the effectiveness of this scheme.