Study On Synchronization Of Time-delayed Chaotic System And Its Experimental Realized

In this paper, the investigation is focus on the synchronization of time delayed chaotic system with uncertain parameters. It is choice the two-dimensional single delayed chaotic system and three-dimensional double delayed R?ssler system as the discipline is due to the importance of the subject. This paper on the basic of the theoretical analysis, the mathematical proving is solved by the Matlab and designing the chaotic electronic circuit. The practicability of the electronic circuit was checked by the Pspice, and realized the synchronization of time delayed chaotic system in the electronic circuit at last.Firstly, the two-dimensional single delayed chaotic system and three-dimensional double delayed R?ssler system were researched by the Functional Analysis theory, the relative electronic circuit was designed by the result of the equivalent electronic circuit state equation that was turned by the time mathematical model of delayed chaotic system. Then, checking the designed circuit diagram by the Pspice and realizing the dynamic behavior of the delayed chaotic system.Secondly, translating the chaotic synchronization into the stability of the synchronization error system created by the synchronizational theory analysis of time delayed chaotic system is more complex than the normal system and it is the one of the most effective investigation method in this range. Using the Functional Analysis and structure of Lyapunov Function to prove the stability of the error system, and the different stability of error system affected by the different Lyapunov, thereby the suitable Lyapunov can produce a simple controller form and the synchronizational result will be better.Thirdly, although the time delayed chaotic system do have delayed state vectors; it is still difficult to focus on designed electronic circuit of time delayed function. Delayed chaotic system always has low frequency, if the designed the electronic circuit of time delayed chaotic system which were under the lower frequency situation, as the author discussed, low-pass filter could be appropriate electronic circuit within time delayed function, which did not only lose the signal of time delayed system, but also can achieve output of signal delayed. Currently, provisional research at the plan of electronic circuit in time delayed chaotic system with certain parameters synchronization, because of the seldom study of the design of electronic circuit in time delayed chaotic system with uncertain parameter synchronization; and focus on system with certain parameters. Thus, this study has practical significant in time delayed chaotic system. This research in connection with time delayed chaotic system in two cases; such as uncertain parameters and certain parameters, and design the electronic circuit to achieve the synchronization in two cases of it. In conclusion, the investigation results in the synchronization of time delayed chaotic system provide the experiment evidence and the relative theoretical analysis. It is mean that the synchronization of time delayed chaotic system is possible used in the confidential communication.