为探讨混沌同步现象和相应的动力学特性,研究了两类特殊的混沌系统即多涡旋混沌系统和分数阶混沌系统的同步.为此,设计了一种非线性反馈控制器,实现了多涡旋类Lorenz的混沌吸引子的投影同步；通过改变投影同步的比例系数,获得了与激励系统相对应的状态变量的任意比例输出.此设计还实现了分数阶超混沌系统的状态向量与任意信号的追踪同步,从而控制分数阶混沌信号趋于期望的周期轨道或平衡点,并实现分数阶混沌系统与整数阶混沌系统的异构追踪同步.最后设计了具有分数阶混沌特性的电路,借助仿真实验证实了分数阶超混沌系统的动力学行为.这些研究结果可以应用于许多领域,例如宏观经济系统的数据分析、保密通讯系统分析与设计等.

In order to discuss the chaotic synchronisation and its corresponding dynamics feature, two special chaotic systems: fractional order chaos system and multi-scroll chaotic attractor were studied. A non-linear feedback controller is designed and the projective synchronization of the multi-scroll Lorenz-like chaotic attractors is accomplished. Via variation of the proportional coefficient of the projective synchronization, an arbitrary ratio-metric of the state variables corresponding to the excitation system is obtained. The state vectors of  the faractional order hyperchaotic system and the arbitrary signals’ synchronized tracking is desigened to control this fractional order’s chaostic signal to expected periodic orbit. So that, the isomer tracking synchronization of the fractional order and integer order chaotic system is achieved initially. In the end, a fractional oder chaotic electronic circuits is designed, and with the help of simulation experiment, the dynamic behavior of this fractional order chaotic system is verified. This research result can be applied to many fields, such as data analysis
in macro-economic system, system analysis and design in confidential conmunicational system and so on.