Reliability of the 0-1 test for chaos

被引:59
|
作者
Hu, J [1 ]
Tung, WW
Gao, JB
Cao, YH
机构
[1] Univ Florida, Dept Elect & Comp Engn, Gainesville, FL 32611 USA
[2] Purdue Univ, Dept Earth & Atmospher Sci, W Lafayette, IN 47907 USA
[3] BioSieve, Campbell, CA 95008 USA
来源
PHYSICAL REVIEW E | 2005年 / 72卷 / 05期
关键词
D O I
10.1103/PhysRevE.72.056207
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
In time series analysis, it has been considered of key importance to determine whether a complex time series measured from the system is regular, deterministically chaotic, or random. Recently, Gottwald and Melbourne have proposed an interesting test for chaos in deterministic systems. Their analyses suggest that the test may be universally applicable to any deterministic dynamical system. In order to fruitfully apply their test to complex experimental data, it is important to understand the mechanism for the test to work, and how it behaves when it is employed to analyze various types of data, including those not from clean deterministic systems. We find that the essence of their test can be described as to first constructing a random walklike process from the data, then examining how the variance of the random walk scales with time. By applying the test to three sets of data, corresponding to (i) 1/f(alpha) noise with long-range correlations, (ii) edge of chaos, and (iii) weak chaos, we show that the test mis-classifies (i) both deterministic and weakly stochastic edge of chaos and weak chaos as regular motions, and (ii) strongly stochastic edge of chaos and weak chaos, as well as 1/f(alpha) noise as deterministic chaos. Our results suggest that, while the test may be effective to discriminate regular motion from fully developed deterministic chaos, it is not useful for exploratory purposes, especially for the analysis of experimental data with little a priori knowledge. A few speculative comments on the future of multiscale nonlinear time series analysis are made.
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页数:5
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