分数阶Liu混沌系统及其电路实验的研究与控制

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. 关键词：分数阶Liu系统电路实验混沌控制

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

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.