动力系统实测数据的Lyapunov指数的矩阵算法

基金项目: 国家自然科学基金资助项目(19672043)

The Matric Algorithm of Lyapunov Exponent for the Experimental Date Obtained in Dynamic Analysis

1.
Department of Economy and M anagement, Tianjin Finance University, Tianjin 300222, P. R. China;
2.
Department of Mechanics, Tianjin University, Tianjin 300072, P. R. China;
3.
Department of Mathematics, Shanghai University, Shanghai 201800, P. R. China

摘要: Lyapunov指数l是定量描述混沌吸引子的重要指标,自从1985年Wolf提出Lyapunov指数l的轨线算法以来,如何准确、快速地计算正的、最大的Lyapunov指数l_max便成为人们关注的问题,虽有不少成功计算的报导,但一般并不公开交流.在Zuo Bingwu理论算法的基础上,给出了Lyapunov指数l的具体的矩阵算法,并与Wolf的算法进行了比较,计算结果表明:算法能快速、准确地计算(主要是正的、最大的)Lyapunov指数l_max.并对Lyapunov指数l的大小所反应的吸引子的特性进行了分析,并得出了相应的结论.
- 非线性混沌时序 /
- Lyaypunov指数l /
- 矩阵算法
Abstract: The Lyapunov exponent is important quantitative index for describing chaotic attractors.Since Wolf put up the trajectory algorithm to Lyapunov exponent in 1985,how to calculate the Lyapunov exponent with accuracy has become a very important question.Based on the theoretical algorithm of Zuo Binwu,the matric algorithm of Lyapunov exponent is given,and the results with the results of Wolf's algorithm are compared.The calculating results validate that the matric algorithm has sufficient accuracy,and the relationship between the character of attractor and the value of Lyapunov exponent is studied in this paper.The corresponding conclusions are given in this paper.
- nonlinear chaotic timeseries /
- Lyapunov exponent /
- matric algorithm

[1]	Wolf Alan,etal.Determining Lyapunov exponentfrom atimeseries[J].Phys D,1985,16:285~317.
[2]	Ellner S.Convergence rates and data requirements for Jacobian-based estimates of Lyapunov exponents from data[J].Phys Lett A,1991,153:357~363.
[3]	Reggie Brown,Paul Bryant.Computing the Lyapunov spectrum of a dynamical system from an observed time series[J].Phys Rev A,1991,43(6):2787~2806.
[4]	Ramazan Gencay,etal.An algorithm forthe N Lyapunov exponents of an N-dimensional unknown dynamical system[J].Phys D,1992,59:142~157.
[5]	Yu Quanhe,etal.Lyapunov exponents of the circle map in human hearts[J].Phys Lett A,1992,170(1):29~32.
[6]	马军海,陈予恕.高斯分布的随机数对动力系统实测数据判值影响的分析研究[J].非线性动力学学报,1997,4(1):25~33.
[7]	Shun Guanwu,etal.The Lyapunov exponent nearthe criticality of type Vintermittency[J].Phys Lett A,1995,197(1):287~292.
[8]	Holger Kantz.Arobust method to estimate the maximal Lyapunov exponent[J].Phys Lett A,1994,185(1):77~87.
[9]	Zuo Binwu.Remark on metric analysis of reconstructed dynamics from chaotictimeseries[J].Phys D,1995,85:485~495.
[10]	Nerenberg M A H.Correlation dimension and systematic geometric effects[J].Phys Rev A,1990,42:7065~7674.