| 动力系统实测数据的Lyapunov指数的矩阵算法 |
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| 引用本文： | 马军海,陈予恕,刘曾荣. 动力系统实测数据的Lyapunov指数的矩阵算法[J]. 应用数学和力学, 1999, 20(9): 919-927 |
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| 作者姓名： | 马军海 陈予恕 刘曾荣 |
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| 作者单位： | 1.天津财经学院管理系, 天津 300222; |
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| 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lmax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lmax.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.
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| 关 键 词： | 非线性混沌时序 Lyaypunov指数l 矩阵算法 |
| 收稿时间： | 1997-05-10 |
The Matric Algorithm of Lyapunov Exponent for the Experimental Date Obtained in Dynamic Analysis |
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| Ma Junhai,Chen Yushu,Liu Zengrong. The Matric Algorithm of Lyapunov Exponent for the Experimental Date Obtained in Dynamic Analysis[J]. Applied Mathematics and Mechanics, 1999, 20(9): 919-927 |
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| Authors: | Ma Junhai Chen Yushu Liu Zengrong |
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| Affiliation: | 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 |
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| 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 are studied in this paper. The corresponding conclusions are given in this paper. |
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| Keywords: | nonlinear chaotic timeseries Lyapunov exponent matric algorithm |
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