Research On Synchronization Of Several Chaotic Systems And A Four-Level Chaotic Secure Communication System

As the mankind moves into the 21st century,nonlinear science is researched more and more thorough, Chaos widely exist in nature as a kind of complex and especial activity forms of nonlinear dynamic system, therefore research on chaos has become a hotspot in recent years. In this paper,the author mainly used mathematical theory proof and numerical simulation software (Matlab) to study several problems of chaos synchronization and design a kind of typical chaotic secure communication system at last. The detailed content of this article can be summarized as follows:(1) The author studied the problem of chaos synchronization for new Lu chaotic system containing constants via three methods as follow:state observer, active control method and Backstepping method. Based on the above three methods, the author designed the adaptive controller based on Lyapunov stability theory which proves that the controller can well realize the asymptotical synchronization between two identical systems. Through numerical simulation, the autuor further verified the effectiveness and advantage of the above three synchronization methods. The author thinks that the synchronization method based on state observer is more flexible and efficient through the comparative analysis of three kinds of synchronization method.(2) Based on the sliding mode control method, the author proposed one kind of modified projective synchronization scheme, and has proven that the method is accuracy theoretically. Based on this, the author has realized the modified projective synchronization between hyper-chaotic Chen system and hyper-chaotic Rossler system. Numerical simulations on the hyper-chaotic Chen system and Rossler system are presented to further verify the effectiveness of the proposed controller.(3) In this part, the generalized synchronization and parameters identification of an uncertain chaotic system is investigated. Based on the invariance principle of differential equations, a systematic method of adaptive control is developed. With this method, parameters identification and generalized synchronization of chaotic systems can be achieved simultaneously. Numerical simulations on the hyper-chaotic Chen system and Lorenz system are presented to verify the effectiveness of the proposed scheme. (4) The author presented a four-level chaotic secure communication system based on PC synchronization of the Unified chaotic system and establishes a dependency between the complexity of the architecture of a secure communication scheme and the efficiency and robustness of security.Taking the Lorenz system as an example, a Multilevel chaotic system has demonstrated a higher degree of security, and to be effective in the restoration of the encryption and transmission of the useful signal by theoretical analysis and numerical simulation of the system.