Study on the parameters determination for reconstructing phase-space in chaos time series

Zhang Shu-Qing; Jia Jian; Gao Min; Han Xu

doi:10.7498/aps.59.1576

Abstract

The choice of delay time and embedding dimension have no correlation in the process of phase-space reconstruction. Based on this principle, a new idea for determining the embedding dimension is proposed. It uses CAO theory after determining the delay time by the mutual information function. Numerical simulations show that the method is applicable for determining the appropriate delay time and the best embedding dimension. The method can recover the original phase space from the time series effectively, and can be used as an effective method to identify the chaotic signal.

Keywords:

Authors and contacts

1.
燕山大学电气工程学院，河北省测试计量技术及仪器重点实验室，秦皇岛 066004

References

[1]	［1］Jiang W L,Zhang S Q,Wang Y Q 2005 Chaos and Wavelet Based Fault Information Diagnosis （Beijing: National Defence Industry Press） p43 （in Chinese）［姜万录、张淑清、王益群 2005 基于混沌和小波的故障信息诊断（北京:国防工业出版社）第43页］
[2]	［2］Liu S Y,Zhu S J,Yu X 2008 Journal of Harbin Engineering Univertity 29 4（in Chinese）［刘树勇、朱石坚、俞翔 2008 哈尔滨工程大学学报 29 4］
[3]	［3］Liu Z H 2006 Fundamentals and Applications of Chaotic Dynamics （Beijing: Higher Education Press） p71 （in Chinese）［刘宗华 2006 混沌动力学基础及其应用（北京:高等教育出版社）第71页］
[4]	［4］Wang J,Shi Y F,Yu H R 2001 Journal of Sichuan University （Engineering Science Edition） 33 2（in Chinese）［王军、石炎福、余华瑞 2001 四川大学学报（工程科学版） 33 2］
[5]	［5］Huang G R,Rui X F 2004 Advances in Water Science15 2（in Chinese）［黄国如、芮孝芳 2004 水科学进展 15 2］
[6]	［6］Li C G,Pei L Q 2003 Acta Phys.Sin. 52 2114（in Chinese）［李春贵、裴留庆 2003 52 2114］
[7]	［7］Wang S,Yang Z A,Ren Z J 2005 Optical Technique 31 5 （in Chinese）［王沙、杨志安、任中京 2005 光学学报 31 5］
[8]	［8］Jiang W L,Zhang S Q,Wang Y Q 2000 Chinese Journal of Mechanical Engineering 36 10（in Chinese）［姜万录、张淑清、王益群 2000 机械工程学报 36 10］
[9]	［9］You R Y,Chen Z,Xu S C,Wu B X 2004 Acta Phys.Sin. 53 2882（in Chinese）［游荣义、陈忠、徐慎初、吴伯僖 2004 53 2882］
[10]	］Yu W B 2008 Calculate Experiment and Analysis on Chaos （Beijing:Science Press） p33 （in Chinese）［于万波 2008 混沌的计算实验与分析（北京:科学出版社）第33页］
[11]	］Sun H Y,Cao Q J 2000 Journal of Shandong University of Technology 30 2（in Chinese）［孙海云、曹庆杰 2000 山东工业大学学报 30 2］
[12]	］Li Y,Yang B J 2007 Chaos Osilator System（L-Y） and Its Detection（Beijing: Science Press） p112 （in Chinese）［李月、杨宝俊 2007 混沌振子系统（L-Y）与检测（北京:科学出版社）第112页］
[13]	］Xiao F H，Yan G R，Han Y H 2005 Acta Phys.Sin. 54 550（in Chinese）［肖方红、阎桂荣、韩宇航 2005 54 550］
[14]	］Chu J F 2006 Chaos and Cycles of Chinese Stock Market （Beijing University） p16 （in Chinese）［储军峰 2006 中国股市的混沌性质研究（北京大学）第16页］
[15]	］Cao L Y 1997 Physica D 110 43
[16]	］Xu X K 2007 Nonlinear Analysis and Modeling on Mixed Sea-wave （Dalian:Dalian Maritime Affairs University） p9 （in Chinese）［许小可 2007 海杂波的非线性分析与建模（大连:大连海事大学）第9页］

Cited By

[1]	［1］Jiang W L,Zhang S Q,Wang Y Q 2005 Chaos and Wavelet Based Fault Information Diagnosis （Beijing: National Defence Industry Press） p43 （in Chinese）［姜万录、张淑清、王益群 2005 基于混沌和小波的故障信息诊断（北京:国防工业出版社）第43页］
[2]	［2］Liu S Y,Zhu S J,Yu X 2008 Journal of Harbin Engineering Univertity 29 4（in Chinese）［刘树勇、朱石坚、俞翔 2008 哈尔滨工程大学学报 29 4］
[3]	［3］Liu Z H 2006 Fundamentals and Applications of Chaotic Dynamics （Beijing: Higher Education Press） p71 （in Chinese）［刘宗华 2006 混沌动力学基础及其应用（北京:高等教育出版社）第71页］
[4]	［4］Wang J,Shi Y F,Yu H R 2001 Journal of Sichuan University （Engineering Science Edition） 33 2（in Chinese）［王军、石炎福、余华瑞 2001 四川大学学报（工程科学版） 33 2］
[5]	［5］Huang G R,Rui X F 2004 Advances in Water Science15 2（in Chinese）［黄国如、芮孝芳 2004 水科学进展 15 2］
[6]	［6］Li C G,Pei L Q 2003 Acta Phys.Sin. 52 2114（in Chinese）［李春贵、裴留庆 2003 52 2114］
[7]	［7］Wang S,Yang Z A,Ren Z J 2005 Optical Technique 31 5 （in Chinese）［王沙、杨志安、任中京 2005 光学学报 31 5］
[8]	［8］Jiang W L,Zhang S Q,Wang Y Q 2000 Chinese Journal of Mechanical Engineering 36 10（in Chinese）［姜万录、张淑清、王益群 2000 机械工程学报 36 10］
[9]	［9］You R Y,Chen Z,Xu S C,Wu B X 2004 Acta Phys.Sin. 53 2882（in Chinese）［游荣义、陈忠、徐慎初、吴伯僖 2004 53 2882］
[10]	］Yu W B 2008 Calculate Experiment and Analysis on Chaos （Beijing:Science Press） p33 （in Chinese）［于万波 2008 混沌的计算实验与分析（北京:科学出版社）第33页］
[11]	］Sun H Y,Cao Q J 2000 Journal of Shandong University of Technology 30 2（in Chinese）［孙海云、曹庆杰 2000 山东工业大学学报 30 2］
[12]	］Li Y,Yang B J 2007 Chaos Osilator System（L-Y） and Its Detection（Beijing: Science Press） p112 （in Chinese）［李月、杨宝俊 2007 混沌振子系统（L-Y）与检测（北京:科学出版社）第112页］
[13]	］Xiao F H，Yan G R，Han Y H 2005 Acta Phys.Sin. 54 550（in Chinese）［肖方红、阎桂荣、韩宇航 2005 54 550］
[14]	］Chu J F 2006 Chaos and Cycles of Chinese Stock Market （Beijing University） p16 （in Chinese）［储军峰 2006 中国股市的混沌性质研究（北京大学）第16页］
[15]	］Cao L Y 1997 Physica D 110 43
[16]	］Xu X K 2007 Nonlinear Analysis and Modeling on Mixed Sea-wave （Dalian:Dalian Maritime Affairs University） p9 （in Chinese）［许小可 2007 海杂波的非线性分析与建模（大连:大连海事大学）第9页］

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Vol. 59, Issue 3 - 2010-02-05

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