Synchronization Of Chaotic Systems Of Fractional Control Method Study

Chaos is a special nonlinear system. In recent years, chaos has attracted attentions of many scholars in Mathematics and control. The research of chaos has been studied deeply. Chaotic systems are sensitive to the initial conditions and the chaos can't be predicted, so it is widely used in many fields, especially in the security of communications.The control of chaos is a crucial to the application of chaos, and the chaos controlled to be synchronized is the important part. As fractional order chaos has more complex characters than the integer order chaos, so it is more worthy to study the fractional order chaos. In this paper the dynamics characteristics of chaos and its synchronization methods are studied.The content of this paper is important for the application of fractional chaos to the data encryption, secure communications etc. All of works in the paper are as follows:(1)First the development and the derivation of chaos are introduced, then the definition and the applications of the fractional order chaotic system are introduced briefly. Some typical concepts and methods of synchronization are introduced, the definition of fractional order systems and its numerical solution are summarizes.Then the paper introduced the stability theorem of the fractional order chaotic system(2) The characteristics of the fractional Chen chaotic systems and the fractional order unified chaotic system are discussed and simulated. After that a controller is designed to makes the two fractional order chaos systems synchronized.(3)Based on the integer-orders Chen-Lee chaotic system, the fractional order Chen-Lee chaos is proposed, and its dynamic characteristics are analyzed. And then a controller is designed using the method of nonlinear feedback to make the drive system and response system synchronized.(4) A new fractional order chaotic system is proposed, and its characteristics of chaos are studied deeply. Then the characteristics of chaos are simulated using the software of Matlab. After that three controllers are designed using the methods of active control, state observer and nonlinear feedback to make the drive system and response system synchronized. After that the correctness and effectiveness of the controllers is proved by the simulation.