分数阶Chen系统的分析、同步及其保密通信实现

摘要

The chaotic behavior of fractional-order Chen system was analyzed by giving the diagram of Lyapunov expo-nents and bifurcation diagram with variation of system parameters,which showed the chaotic characteristics of the system from numerical analysis point of view.After that,based on a design method for synchronization of chaotic system by using observers,a synchronization control scheme for the fractional-order Chen system was presented,and the effectiveness of the synchronization control was then proved through theoretical analysis and numerical simulation.In addition,an analog circuit was also designed to implement the synchronization control.The results observed in oscillation indicate that the synchroniza-tion method can synchronize the response system and driving system very well.At last,based on the above research, confidential communications was studied by using the analog synchronization circuit of fractional-order Chen system. The results show that both the synchronization control and its imlementation in confidential communications are feasible.%首先分析分数阶Chen系统的混沌行为，给出系统随参数变化的Lyapunov指数谱图和分岔图，从数值分析上说明了其混沌特性。然后基于一类混沌系统的观测器设计方法，给出了分数阶Chen系统的混沌同步控制策略，并分析和验证了该同步方法的有效性。另外，用模拟电路实现了该同步控制。示波器观测结果表明，该同步方法能够使驱动系统和响应系统达到很好的同步效果。在上述研究的基础上，利用分数阶 Chen 系统的同步电路进行了模拟信号的保密通信研究，结果表明，该同步控制及其保密通信方法是可行的。