A complexity measure approach based on forbidden patterns and correlation degree

doi:10.1088/1674-1056/19/6/060515

中国物理B ›› 2010, Vol. 19 ›› Issue (6): 60515-060515.doi: 10.1088/1674-1056/19/6/060515

A complexity measure approach based on forbidden patterns and correlation degree

王福来

Department of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310012, China

收稿日期:2009-09-09 出版日期:2010-06-15 发布日期:2010-06-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No.~10871168).

A complexity measure approach based on forbidden patterns and correlation degree

Wang Fu-Lai(王福来)^†

Department of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou 310012, China

Received:2009-09-09 Online:2010-06-15 Published:2010-06-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No.~10871168).

摘要/Abstract

摘要： Based on forbidden patterns in symbolic dynamics, symbolic subsequences are classified and relations between forbidden patterns, correlation dimensions and complexity measures are studied. A complexity measure approach is proposed in order to separate deterministic (usually chaotic) series from random ones and measure the complexities of different dynamic systems. The complexity is related to the correlation dimensions, and the algorithm is simple and suitable for time series with noise. In the paper, the complexity measure method is used to study dynamic systems of the Logistic map and the H\'enon map with multi-parameters.

Abstract: Based on forbidden patterns in symbolic dynamics, symbolic subsequences are classified and relations between forbidden patterns, correlation dimensions and complexity measures are studied. A complexity measure approach is proposed in order to separate deterministic (usually chaotic) series from random ones and measure the complexities of different dynamic systems. The complexity is related to the correlation dimensions, and the algorithm is simple and suitable for time series with noise. In the paper, the complexity measure method is used to study dynamic systems of the Logistic map and the H\'enon map with multi-parameters.

Key words: complexity theory, forbidden words, symbolic dynamics, correlation dimensions

中图分类号: (Time series analysis)

05.45.Tp

02.30.Lt (Sequences, series, and summability) 05.40.Ca (Noise) 02.30.Uu (Integral transforms)

王福来. A complexity measure approach based on forbidden patterns and correlation degree[J]. 中国物理B, 2010, 19(6): 60515-060515.

Wang Fu-Lai(王福来). A complexity measure approach based on forbidden patterns and correlation degree[J]. Chin. Phys. B, 2010, 19(6): 60515-060515.

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A complexity measure approach based on forbidden patterns and correlation degree

A complexity measure approach based on forbidden patterns and correlation degree

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