三种动力系统Lyapunov指数的比较

THE COMPARISON OF LYAPUNOV EXPONENT FOR THREE KINDS OF EXPERIMENTAL DATA OBTAINED FROM DIFFERENT DYNAMIC SYSTEMS

Ｌｙａｐｕｎｏｖ指数是定量描述混沌吸引子的重要指标，自从１９８５年Ｗｏｌｆ提出Ｌｙａ－ｐｕｎｏｖ指数的轨线算法［１］以来，如何准确、快速地计算实验数据的Ｌｙａｐｕｎｏｖ指数便成为一个判定运动性质的重要问题．本文基于作者给出的Ｌｙａｐｕｎｏｖ指数的具体算法，计算了三种动力系统的Ｌｙａｐｕｎｏｖ指数并与Ｗｏｌｆ的算法进行了比较，计算结果表明：不同的Ｌｙａｐｕｎｏｖ指数对应不同的非线性混沌动力系统，且Ｌｙａｐｕｎｏｖ指数越大对应的混沌动力系统的几何结构就越复杂．

The Lyapunov exponent is an important quantitative index for describing chaotic attractors.Since Wolf put up the trajectory algorithm to the Lyapunov exponent in 1985,how to calculate the Lyapunov exponent for the non linear chaotic experimental data obtained in dynamic analysis accurately has become a very important question.Based on the theoretical algorithm of paper,this paper gives the matric algorithm of the Lyapunov exponent,and compares its results with the results of Wolfs algorithm.The calculated results validate that different Lyapunov exponents correspond to the different behavior of the non linear chaotic dynamic system,and Lyapunov exponents are bigger,and the structure of the chaotic behavior is more complex.