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Identifying the linear region based on machine learning to calculate the largest Lyapunov exponent from chaotic time series

文献类型：期刊论文

作者Zhou, Shuang1,2,3; Wang, Xingyuan1,4
刊名CHAOS
出版日期2018-12-01
卷号28期号:12页码:7
ISSN号1054-1500
DOI10.1063/1.5065373
通讯作者Wang, Xingyuan(xywang@dlmu.edu.cn)
英文摘要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.
资助项目National Natural Science Foundation of China[61672124] ; National Natural Science Foundation of China[61370145] ; National Natural Science Foundation of China[61173183] ; Password Theory Project of the 13th Five-Year Plan National Cryptography Development Fund[MMJJ20170203] ; Research Project of Chongqing Normal University[17XLB001] ; Research Project of Chongqing Normal University[16XYY21]
WOS研究方向Mathematics ; Physics
语种英语
WOS记录号WOS:000454619500023
出版者AMER INST PHYSICS
源URL[http://119.78.100.138/handle/2HOD01W0/7255]  
专题中国科学院重庆绿色智能技术研究院
通讯作者Wang, Xingyuan
作者单位1.Dalian Univ Technol, Fac Elect Informat & Elect Engn, Dalian 116024, Peoples R China
2.Chongqing Normal Univ, Sch Math Sci, Chongqing 401331, Peoples R China
3.Chinese Acad Sci, Chongqing Inst Green & Intelligent Technol, Chongqing Key Lab Addit Mfg Technol & Syst, Chongqing 400714, Peoples R China
4.Dalian Maritime Univ, Sch Informat Sci & Technol, Dalian 116026, Peoples R China
推荐引用方式
GB/T 7714		 Zhou, Shuang,Wang, Xingyuan. Identifying the linear region based on machine learning to calculate the largest Lyapunov exponent from chaotic time series[J]. CHAOS,2018,28(12):7.
APA Zhou, Shuang,&Wang, Xingyuan.(2018).Identifying the linear region based on machine learning to calculate the largest Lyapunov exponent from chaotic time series.CHAOS,28(12),7.
MLA Zhou, Shuang,et al."Identifying the linear region based on machine learning to calculate the largest Lyapunov exponent from chaotic time series".CHAOS 28.12(2018):7.

入库方式： OAI收割

来源：重庆绿色智能技术研究院

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