分数阶Liu混沌系统及其电路实验的研究与控制  

Study on the fractional-order Liu chaotic system with circuit experiment and its control

作　　者：陈向荣[1] 刘崇新[1] 王发强[1] 李永勋[1] 

机构地区：[1]西安交通大学电气工程学院,电力设备电气绝缘国家重点实验室,西安710049

出　　处：《物理学报》2008年第3期1416-1422,共7页Acta Physica Sinica

摘　　要：基于波特图的频域近似方法,研究了分数阶Liu混沌系统,并设计了一种树形电路单元来实现分数阶Liu混沌系统,通过对2.7阶Liu混沌系统的电路仿真和实验,以及α=0.8—0.1(步长0.1)Liu混沌系统的电路仿真,验证了树形电路单元的有效性,证实分数阶Liu混沌系统中确实存在混沌现象,且存在混沌的最低阶数为0.3.设计简单有效的线性反馈控制器,实现了分数阶Liu混沌系统的混沌控制.In this paper, applying frequency domain techniques based on Bode diagram, fractional-order Liu chaotic system is studied. An electronic circuit unit of tree shape is designed to realize the fractional-order chaotic Liu system. Circuit experiment of 2.7- order Liu system, as well as simulation results of fractional-order Liu chaotic system with α = 0.8-0.1 in step size of 0. 1 , verify the circuit unit＇s effectiveness, and prove that chaos actually exists in the fractional-order Liu chaotic system with order as low as 0. 3. A simple, but effective linear feedback controller is designed to realize the chaotic control of fractional-order Liu chaotic system.

关 键 词：分数阶Liu系统 电路实验 混沌控制 分数阶微分 

分 类 号：O415.5[理学—理论物理]