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Identifying the linear region based on machine learning to calculate the largest Lyapunov exponent from chaotic time series
Zhou, Shuang1,2,3; Wang, Xingyuan1,4
2018-12-01
摘要To reduce the error caused by the human factor, this paper proposes a modification of a well-known small data method to obtain the largest Lyapunov exponent more accurately, which is based on machine learning for better identification of linear region. Firstly, we use the k-d tree neighborhood search algorithm to improve the computational efficiency of the average divergence index data. Secondly, the unsaturated data are obtained by the density peak based clustering algorithm from the average divergence index data. Thirdly, we use the density peak based clustering algorithm to identify the linear region from the first-order difference curve of the retained data. Finally, the largest Lyapunov exponent is obtained by using the least squares method to fit the linear region. Our method is applied to simulate five famous theoretical chaotic systems, the results show that the proposed method can automatically identify the linear region, which is more accurate than the small data method for the largest Lyapunov exponent calculation and the effectiveness of our method is verified through the simulation of two real-world time series. Published by AIP Publishing.
DOI10.1063/1.5065373
发表期刊CHAOS
ISSN1054-1500
卷号28期号:12页码:7
通讯作者Wang, Xingyuan(xywang@dlmu.edu.cn)
收录类别SCI
WOS记录号WOS:000454619500023
语种英语