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.
Received: 26 July 2008
Revised: 27 April 2009
Accepted manuscript online:
(Fluctuation phenomena, random processes, noise, and Brownian motion)
Fund: 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).
Cite this article:
Wang Fu-Lai(王福来) and Yang Hui-Huang(杨辉煌) An improvement on measure methods of the complexity theory and its applications 2009 Chin. Phys. B 18 4042
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