A novel method based on the fuzzy C-means clustering to calculate the maximal Lyapunov exponent from small data

doi:10.7498/aps.65.020502

CORC > 重庆绿色智能技术研究院 > 中国科学院重庆绿色智能技术研究院 > 自动推理与认知研究中心

	A novel method based on the fuzzy C-means clustering to calculate the maximal Lyapunov exponent from small data
	Zhou Shuang 1,2; Feng Yong1 ; Wu Wen-Yuan1 ; Wang Wei-Hua 1,2
刊名	ACTA PHYSICA SINICA
	2016-01-20
卷号	65 期号:2 页码:7
关键词	maximal Lyapunov exponent linear region fuzzy C-means clustering
ISSN号	1000-3290
DOI	10.7498/aps.65.020502
通讯作者	Zhou, S (reprint author), Chinese Acad Sci, Chongqing Key Lab Automated Reasoning & Cognit, Chongqing Inst Green & Intelligent Technol, Chongqing 400714, Peoples R China. ; Zhou, S (reprint author), Univ Chinese Acad Sci, Beijing 100049, Peoples R China.
英文摘要	In order to reduce errors caused by human factors to identify the linear region, we propose a new method based on the fuzzy C-means clustering for calculating the maximum Lyapunov exponent from small data. The method based on the changing characteristic of average divergence index curve is used to identify the linear region. Firstly, the average divergence index data are calculated from the small data algorithm for the given chaotic time series. Secondly, the fuzzy C-means clustering method is used for dividing the data into two classes (unsaturated and saturated data), and the unsaturated data are retained. Thirdly, the retained data are divided by the same clustering method into three classes (positive fluctuation data, zero fluctuation data and negative fluctuation data), and the zero fluctuation data are retained. Fourthly, the 3 sigma criterion is used for excluding gross errors to retain the valid from the selected data. Finally, the regression analysis and statistical test are used to identify the linear region from the valid data. The effectiveness of the proposed method can be demonstrated by the famous chaotic systems of Logistic and Henon. The calculated results are close to the theoretical values than the subjective method. Experimental results show that the proposed new approach is easier to operate, more efficient and more accurate as compared with the subjective recognition. But this method has its own shortcomings. 1) As the new method is verified by the simulation experiment, there exists no strict mathematical proof. 2) Since the difference algorithm is used in this new method, it will miss some detailed information in some cases. 3) The calculation accuracy still needs to be improved, so this method only serves as a reference to detect the linear region, it can not be applied to high precision engineering field. Considering the deficiencies of the new method, we will make further research to improve the calculation method for maximum Lyapunov exponent, so as to make it solve the real-time problem of the signal detection, and find the accurate location of abrupt climate change in the field of meteorology, to provide accurate satellite launch safety period in the field of space weather and other aspects. In short, studying the largest Lyapunov exponent from chaotic time series has a wide application prospect and practical significance.
资助项目	National Natural Science Foundation of China[11301524] ; Chongqing Academicians Special Project Based on the Basic and Frontier Reaearches, China[cstc2015jcyjys40001]
WOS研究方向	Physics
语种	英语
出版者	CHINESE PHYSICAL SOC
WOS记录号	WOS:000370942000006
内容类型	期刊论文
源URL	[http://119.78.100.138/handle/2HOD01W0/2271]
专题	自动推理与认知研究中心
通讯作者	Zhou Shuang
作者单位	1.Chinese Acad Sci, Chongqing Key Lab Automated Reasoning & Cognit, Chongqing Inst Green & Intelligent Technol, Chongqing 400714, Peoples R China 2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
推荐引用方式 GB/T 7714	Zhou Shuang,Feng Yong,Wu Wen-Yuan,et al. A novel method based on the fuzzy C-means clustering to calculate the maximal Lyapunov exponent from small data[J]. ACTA PHYSICA SINICA,2016,65(2):7.
APA	Zhou Shuang,Feng Yong,Wu Wen-Yuan,&Wang Wei-Hua.(2016).A novel method based on the fuzzy C-means clustering to calculate the maximal Lyapunov exponent from small data.ACTA PHYSICA SINICA,65(2),7.
MLA	Zhou Shuang,et al."A novel method based on the fuzzy C-means clustering to calculate the maximal Lyapunov exponent from small data".ACTA PHYSICA SINICA 65.2(2016):7.