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The Comparison for Lyapunov Exponents Calculation Methods(PDF)

南京师范大学学报（工程技术版）[ISSN:1006-6977/CN:61-1281/TN]

Issue:
2012年01期
Page:
5-9
Research Field:
Publishing date:

Info

Title:
The Comparison for Lyapunov Exponents Calculation Methods
Author(s):
Zhang Hailong; Min Fuhong; Wang Enrong
School of Electrical and Automation Engineering,Nanjing Normal University,Nanjing 210042,China
Keywords:
Lyapunov exponents; Lorenz system; chaos system
PACS:
O415.5
DOI:
-
Abstract:
In this paper，the several computational methods of Lyapunov exponents are compared，i． e． ，the definition method，the orthogonal method，the wolf method and the small data sets． The Lyapunov exponent power and the max- Lyapunov exponent are computed through the above methods for Lorenz system． From the results，the accuracies and the complexity of the above methods are investigated． Furthermore，the max-Lyapunov exponents are also calculated for the chaotic time series including the noise． Finally，numerical results demonstrate that the performances of different computational methods have differences，and some summaries will be presented．

References:

［1］吕金虎，陆君安，陈士华． 混沌时间序列分析及其应用［M］． 武汉: 武汉大学出版社， 2005． Lü Jinhu，Lu Junan，Chen Shihua． The Analysis and Application for Chaotic Time Series［M］． Wuhan: Wuhan University Press，2005． ( in Chinese)
［2］罗利军，李银山，李彤，等． 李雅普诺夫指数谱的研究与仿真［J］． 计算机仿真， 2005，22( 12) : 285-288． Luo Lijun，Li Yinshan，Li Tong，et al． Research and simulation of Lyapunov’s exponents［J］． Computer Simulation， 2005， 22 ( 12) : 285-288． ( in Chinese)
［3］严雯，逯宗胜． Lyapunov 指数的数值计算方法［J］． 中国对外贸易，2010，55( 24) : 354． Yan Wen，Lu Zongsheng． The numerical calculation method of Lyapunov index［J］． China’s Foreign Trade， 2010，55( 24) : 354-356． ( in Chinese)
［4］廖德玮，朱伟强． Lyapunov 指数计算研究及应用［J］． 温州职业技术学院学报， 2008，8 ( 4) : 39-41． Liao Dewei，Zhu Weiqiang． Research on lyapunov exponents algorithm and its application［J］． Journal of Wenzhou Vocational and Thechnical College， 2008，8 ( 4) : 39-41． ( in Chinese)
［5］王妍，徐伟，曲继圣． 基于时间序列的相空间重构算法及验证( 一) ［J］． 山东大学学报: 工学版， 2005， 35( 6) : 89-94． Wang Yan，Xu Wei，Qu Jisheng． The algorithm and chick of phase-space reconstruction based on the time series［J］． Journal of Shangdong University: Engineering Science Edition， 2005， 35( 6) : 89-94． ( in Chinese)
［6］Xie Zhongyu，Wang Kejun，Zhang Ling． Improved algorithm for calculating Lyapunov exponent and distinguishing chaos from noise［J］． Journal of Harbin Institute of Technology，2010，17( 1) : 101-104．
［7］张政伟． 用Matlab 分析Lorenz 系统族［J］． 现代电子技术， 2004， 31( 6) : 40-42． Zhang Zhengwei． Analysis of Lorenz system family with MATLAB［J］． Contemporary Electric Technique， 2004， 31( 6) : 40-42． ( in Chinese)
［8］ Lu Zhenbo，Cai Zhiming． Determination of embedding parameters for phase space reconstruction based on improved C － C methed［J］． Journal of System Simulation，2007， 11( 19) : 2 527-2 538．
［9］陈国华，马军海，盛昭瀚． 动力系统实测数据相空间重构的改进方法［J］． 东南大学学报: 自然科学版，2000， 30( 1) : 16-21． Chen Guohua，Ma Junhai，Sheng Shaohan． A new algorithm of the phase space reconstruction for the data obtained in dynamical systems［J］． Journal of Southeast University: Natural Science Edition， 2000，30( 1) : 16-21． ( in Chinese)
［10］韩敏，王一颉． 含噪声混沌信号最大Lyapunov 指数计算［J］． 控制理论与应用， 2008， 25( 5) : 898-900． Han Min，Wang Yijie． Computation of the largest Lyapunov exponent in noisy chaotic signal［J］． Control Theory and Applications， 2008， 25( 5) : 898-900． ( in Chinese)

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Last Update: 2013-03-11