一类整数阶分数阶单摆系统的混沌同步

Chaos Synchronization of a Class of Simple Pendulum Systems of Integer-Order and Fractional-Order

基于驱动．响应法，根据Lyapunov稳定性理论和分数阶微积分的相关理论研究了一类整数阶，分数阶单摆系统的混沌同步问题，针对无阻尼和有阻尼两种情况给出了控制律的设计，并给出了严格的数学证明和推理过程，研究表明一定条件下，选取适当的控制律单摆系统的主从系统是混沌同步的，最后数值仿真说明方法有效．

The problem of chaos Synchronization for a class of simple pendulum systems is studied usingLyapunov stability theory and fractional-order caculurs theory based on driveresponse approach. The control law is designed and strict proof and conclusion in mathematics is given out for undamped and damped two cases in the paper. The conclusion is arrived that master-slave systems of simple pendulum systems are chaos synchronized under appropriate controlling law. Numerical simulations of chaotic system verify the effectiveness of the proposed method.