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Applied Mathematics and Mechanics (English Edition) ›› 1999, Vol. 20 ›› Issue (9): 985-993.

• 论文 • 上一篇    下一篇

THE MATRIC ALGORITHM OF LYAPUNOV EXPONENT FOR THE EXPERIMENTAL DATA OBTAINED IN DYNAMIC ANALYSIS

马军海1, 陈予恕2, 刘曾荣3   

  1. 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
  • 收稿日期:1997-05-10 修回日期:1999-03-05 出版日期:1999-09-18 发布日期:1999-09-18
  • 基金资助:

    the National Natural Science Foundation of China(19672043)

THE MATRIC ALGORITHM OF LYAPUNOV EXPONENT FOR THE EXPERIMENTAL DATA OBTAINED IN DYNAMIC ANALYSIS

Ma Junhai1, Chen Yushu2, Liu Zengrong3   

  1. 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
  • Received:1997-05-10 Revised:1999-03-05 Online:1999-09-18 Published:1999-09-18
  • Supported by:

    the National Natural Science Foundation of China(19672043)

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摘要： 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.

关键词: nonlinear chaotic timeseries, Lyapunov exponent, matric algorithm

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.

Key words: nonlinear chaotic timeseries, Lyapunov exponent, matric algorithm

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