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应用科学学报 ›› 2003, Vol. 21 ›› Issue (2): 127-131.

• 论文 • 上一篇    下一篇

时间序列最大Lyapunov指数的计算

李国辉1, 徐得名2, 周世平1   

  1. 1 上海大学通信与信息工程学院 上海 200436;
    2 上海大学理学院 上海 200072
  • 收稿日期:2002-04-19 修回日期:2002-06-25 出版日期:2003-06-10 发布日期:2003-06-10
  • 作者简介:李国辉(1971-),男,湖南衡阳人,讲师,博士.周世平(1959-),男,安徽阜阳人,教授,博导;徐得名(1934-),男.浙江衙州人,教授,博导.
  • 基金资助:
    国家自然科学基金(69871016)

Computing the Largest Lyapunov Exponent from Time Series

LI Guo-hui1, ZHOU Shi-ping2, XU De-ming1   

  1. 1 School of Communication and Information Engineering, Shanghai University, Shanghai 200072, China;
    2 School of Science, Shanghai University, Shanghai 200436, China
  • Received:2002-04-19 Revised:2002-06-25 Online:2003-06-10 Published:2003-06-10

PDF

304

被引次数

63

摘要： 从Lyapunov指数的定义出发,研究了一种快速、高效计算时间序列最大Lyapunov指数方法。通过对几种已知模型的数值模拟表明:最大Lyapunov指数与重构相空间的维数和延迟时间在较大的变化范围能很好符合,重构相空间所需的数据较少,维数较低,使计算在结果保持准确的前提下大大简化。

关键词: Lyapunov指数, 时间序列, 相空间重构

Abstract: A method to calculate the largest Lyapunov exponent from the observed time series based on its definition is proposed. We have tested it on several known systems, such as the Logistic model, the Henon mapping and the Lorenz system. It is found that the estimated largest Lyapunov exponent from time series has a reasonable good accuracy. More remarkably, the simulation result is independent of the embedding dimension and the delay time to a certain extent. The shorter data and the lower dimension of phase space simplify the computation without significant loss of precision.

Key words: Lyapunov exponent, phase space reconstruction, time series

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