中国物理B ›› 2009, Vol. 18 ›› Issue (9): 4042-4048.doi: 10.1088/1674-1056/18/9/071

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An improvement on measure methods of the complexity theory and its applications

王福来, 杨辉煌   

  1. Department of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310012, China
  • 收稿日期:2008-07-26 修回日期:2009-04-27 出版日期:2009-09-20 发布日期:2009-09-20
  • 基金资助:
    Project supported by the Scientific Research Fund of Zhejiang Provincial Education Department of China (Grant No 20070814) and the National Natural Science Foundation of China (Grant No 10871168).

An improvement on measure methods of the complexity theory and its applications

Wang Fu-Lai(王福来)† and Yang Hui-Huang(杨辉煌)   

  1. Department of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310012, China
  • Received:2008-07-26 Revised:2009-04-27 Online:2009-09-20 Published:2009-09-20
  • Supported by:
    Project supported by the Scientific Research Fund of Zhejiang Provincial Education Department of China (Grant No 20070814) and the National Natural Science Foundation of China (Grant No 10871168).

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摘要： A new method is proposed to transform the time series gained from a dynamic system to a symbolic series which extracts both overall and local information of the time series. Based on the transformation, two measures are defined to characterize the complexity of the symbolic series. The measures reflect the sensitive dependence of chaotic systems on initial conditions and the randomness of a time series, and thus can distinguish periodic or completely random series from chaotic time series even though the lengths of the time series are not long. Finally, the logistic map and the two-parameter Henón map are studied and the results are satisfactory.

Abstract: A new method is proposed to transform the time series gained from a dynamic system to a symbolic series which extracts both overall and local information of the time series. Based on the transformation, two measures are defined to characterize the complexity of the symbolic series. The measures reflect the sensitive dependence of chaotic systems on initial conditions and the randomness of a time series, and thus can distinguish periodic or completely random series from chaotic time series even though the lengths of the time series are not long. Finally, the logistic map and the two-parameter Henón map are studied and the results are satisfactory.

Key words: complexity theory, complexity, dynamic system, chaos

中图分类号:  (Time series analysis)

  • 05.45.Tp
05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion)