The Synchronization And Controlling Circuit Of The Time-delayed Chaotic System

Researching the problems of dynamic system with time-delay is one of the leading edge topics in nonlinear dynamics domains. A time–delayed dynamic system can be able to portray the features more precisely and depict the essence of complexity of things. Time-delayed chaotic system is an infinite dimension system. In the process of synchronization, it overcomes the shortage of nondelay chaotic system with huge dimension and complex structure, and it can also increase safety for secure communication. Synchronization and controlling of the delayed chaotic system are researched by means of circuit experiments, as well as theoretic analysis and numerical calculation. At last, it ends with respective reasonable conclusion to problems of the delayed chaotic system.Firstly, based on the theoretic analysis and numerical calculation, chaos characteristic of the delayed chaotic system is obtained, and a route from double period bifurcation to chaos is observed. Secondly, the delayed circuit was realized in circuit experiment. Using the time delay unit electric circuit which builds has constructed the time delay chaos circuitry, and compares, the experimental result with the value computed result which obtains with the value computed result basically consistent, has confirmed the system chaos characteristic, and has proven the time delay unit electric circuit practical validity. At last, the methods of variable synchronization chaos, such as, Synchronization of variable feedback, Synchronization of disturbance parameters and Synchronization of single variable actuation are applied to the system in circuit experiment, and the numerical calculation results are in good agreement with circuit experiment results. Finally, separately uses in the linear feedback control method and the phase space compression method the time delay chaos circuitry the control, obtained the good control effect. To the linear feedback control method, gives the controllability condition, and gives in the value simulation and the electric circuit experiment the systems control cycle condition result.This article findings provided the theory basis for the actual control chaos, the time-delay chaos system have also provided a very good platform for the chaos practical application.