A complexity measure approach based on forbidden patterns and correlation degree

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

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.

Keywords: complexity theory forbidden words symbolic dynamics correlation dimensions

Received: 09 September 2009
Accepted manuscript online:

PACS:	05.45.Tp	(Time series analysis)
	02.30.Lt	(Sequences, series, and summability)
	05.40.Ca	(Noise)
	02.30.Uu	(Integral transforms)

Fund: Project supported by the National Natural Science Foundation of China (Grant No.~10871168).

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Wang Fu-Lai(王福来) A complexity measure approach based on forbidden patterns and correlation degree 2010 Chin. Phys. B 19 060515

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