分数阶Qi混沌系统投影同步和电路实现

Circuit implementation and project synchronization of fractional-order Qi chaotic systems

对于含有三次非线性项的复杂Qi混沌系统,基于频率近似法研究了其分数阶的混沌动力学行为.通过构造合适的控制方案,实现初始值不同的2个分数阶Qi混沌系统的投影同步,并基于分数阶系统的稳定性理论,通过选择合适的控制参数,使得分数阶误差系统渐进稳定.通过改变投影同步的比例因子,可以获得任意比例于驱动系统混沌信号的信号,这为混沌系统在保密通信等方面的应用提供了技术基础.另外,利用电路仿真软件Multisim10,构造等级模块,设计了主电路驱动系统和子电路响应系统的电路图,实现了初始值不同的2个分数阶Qi混沌系统投影同步,电路实验进一步证实了理论分析和数值仿真的有效性.

The chaotic behaviors in the fractional-order Qi system are first studied using frequency domain technique,in which each equation in the system contains a three-term cross product.Based on the suitable control scheme and the stability criterion of fractal-order linear systems,a simple feedback control method is proposed to realize the project synchronization for two fractional-order Qi chaotic systems with different initial values.The control parameter which makes the error system stable is flexible and easy to choose.The technique can also direct the different scaling factor to gain a desired value which is proportional to the driver system's chaotic signal,and it provides a foundation for the application of chaotic system in secure communications.In addition,the electronic circuits of driver system and response system are designed respectively to realize the project synchronization of the fractional-order Qi chaotic system using the software Multisim 10.The results of circuit experiments verify the effectiveness of numerical simulation.