混沌时序相空间重构的分析和应用研究

马军海; 陈予恕

混沌时序相空间重构的分析和应用研究

马军海¹,
陈予恕²

1.
天津大学管理学院, 天津 300072;
2.
天津大学力学系, 天津 300072

基金项目: 国家自然科学基金资助(19990510)

详细信息

作者简介:
马军海(1965- ),男,教授,博士后;陈予恕(1931- ),男,山东肥城人,教授,博导.俄国科学院外藉院士.

中图分类号: O175.4;O241.81
计量
- 文章访问数: 2377
- HTML全文浏览量: 103
- PDF下载量: 1490
- 被引次数: 0
出版历程
- 收稿日期: 1999-07-12
- 修回日期: 2000-06-25
- 刊出日期: 2000-11-15

An Analytic and Application to State Space Reconstruction About Chaotic Time Series

MA Jun-hai¹,
CHEN Yu-shu²

1.
School of Management, Tianjin University, Tianjin 300072, P R China;
2.
Department of Mechanics, Tianjin University, Tianjin 300072, P R China

摘要

摘要: 在国内外学者工作的基出上,应用Legendere坐标法重构动力系统的相空间,研究了时序时隔τ的取值范围,讨论了时序间隔τ对相空间重构工作的影响,并用所提方法重构了系统的吸引子.算例表明所提方法是有效的.
- 混沌时序 /
- 相空间重构 /
- Legendre坐标法
Abstract: The state space reconstruction is the major important quantitative index for describing nonlinear chaotic time series.Based on the work of many scholars,such as:N.H.Packard,F.Takens M.Casdagli J.F.Bibson,CHEN Yu-shu et al,the state space was reconstructed using the method of Legendre coordinate.Several different scaling regimes for lag time τ were identified.The influence for state space reconstruction of lag time τ was discussed.The result tells us that is a good practical method for state space reconstruction.
- chaotic time series /
- state space reconstruction /
- Legendre coordinates

HTML全文

参考文献(15)

[1]	Packard N H,Crutchifield J P,Farmer J D,et al.Geometry from a time series[J].Phys Rev Lett,1980,45(6):712-716.
[2]	Takens F,Mane.Detecting strange attractors in fluid turbulence[A].In:Rand D A,Young L S,Eds.Dynamical Systems and Turbulence[C].Vol.898 of Lecture Notes in Mathematics,Berlin:Springer,1986,366.
[3]	Berndt Pilgram,Kaplan Daniel T.A comparison of estimators for 1/f noise[J].Phys D,1998,114(3):108-122.
[4]	Casdagli M,Eubank S,Farmer J D,et al.State space reconstruction in the presence of noise[J].Phys D,1991,51(1):52-98.
[5]	YING Cheng-lai,David Lerner.Effective scaling regime for computing the correlation dimension from chaotic time series[J].Phys D,1998,115(5):1-18.
[6]	Badii R,Broggi G,Derighetti B,et al.Dimension increase in filtered chaotic signals[J].Phys Rev Lett,1988,60(4):979-984.
[7]	Mitschke F.A causal filters for chaotic signals[J].Phys Rev A,1990,41:1169-1171.
[8]	Scargle J D.Studies in astronomical time series analysis,Modeling chaotic and random processes with linear filters[J].Astrophys J,1990,359(12):469-482.
[9]	Broomherd D S.Extracting qualitatire dynamics from experimental data[J].Phys D,1987,20(11):217-236.
[10]	Gibson J F,Casdagli M,Eubank S,et al.An analystic approach to proctical state space reconstruction[J].Phys D,1992,57(7):1-30.
[11]	Liebert W,Pawalzik K,Schuster H G.Optimal embeddings of chaotic attractors from topological considerations[J].Europ Phy sics Lett,1991,14(8):521-526.
[12]	CHEN Yu-shu,MA Jun-hai,LIU Zeng-rong.The state space reconstruction technology of different kinds of chaotic data obtained from dynamical system[J].Acta M echan ica Sin ica,1999,15(1):82-92.
[13]	马军海.混沌时序动力系统非线性重构[D].天津:天津大学力学系,1997.
[14]	YING Cheng-lai,David Lerner.Effective scaling regime for computing the correlation dimension from chaotic time series[J].Phys D,1998,115(5):1-18.
[15]	Theiler J.Statistical precision of dimension estimators[J].Phys Rev A,1990,41(6):3038-3051.