Selection of embedding dimension and delay time in phase space reconstruction

Hsi-An Chiao Tung Ta Hsueh/Journal of Xi'an Jiaotong University

Volumn 38, Issue 4, 2004, Pages 335-338

  Ma, Hongguang ^a   Li, Xihai ^b   Wang, Guohua ^b   Han, Chongzhao ^a   Xu, Jianfeng ^b   Zhu, Xiaofei ^b  

^a XI'AN JIAOTONG UNIVERSITY   (China)

^b XI'AN RESEARCH INSTITUTE OF HIGH TECHNOLOGY   (China)

Author keywords

Delay time; Embedding dimension; Multiple autocorrelation; Phase space reconstruction

Indexed keywords

CHAOS THEORY; CORRELATION METHODS; DELAY CONTROL SYSTEMS; ITERATIVE METHODS; TIME SERIES ANALYSIS;

AVERAGE DISPLACEMENT; DELAY TIME; EMBEDDING DIMENSION; INVARIANTS; MULTIPLE AUTOCORRELATION; PHASE SPACE RECONSTRUCTION;

PHASE SPACE METHODS;

EID: 3042726875     PISSN: 0253987X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. Packard N H, Crutchfield J P, Farmer J D, et al. Geometry from a time series [J]. Phys Rev Lett, 1980, 45(3): 712-716.
2. Takens F. Detecting strange attractor in turbulence [J]. Lecture Notes in Mathematics, 1981, 898(2): 361-381
3. Albano A M. SVD and Grassberger-Procaccia algorithm [J]. Phy Rev: A, 1988, 38(20): 3017-3026.
4. Fraser A M. Information and entropy in strange attractors [J]. IEEE Trans on IT Mar, 1989, 35(2): 245-262.
5. Albano A M. Using high-order correlations to define an embedding window [J]. Physica: D, 1991, 54(1): 85-97.
6. Buzug P T. Optimal delay time and embedding dimension for delay-time coordinates by analysis of the global static and local dynamical behavior of strange attractors [J]. Phy Rev: A, 1992, 45(10): 7073-7084.
7. Buzug P T. Comparison of algorithms calculating optimal embedding parameters for delay time coordinates [J]. Physica: D, 1992, 58(2): 127-137.
8. Rossenstein M T, Colins J J, De Luca C J. Reconstruction expansion as a geometry-based framework for choosing proper delay times [J]. Physica: D, 1994, 73(1): 82-98.
9. Kember G, Fowler A C. A correlation function for choosing time delays in phase portrait reconstructions [J]. Phy Lett: A, 1993, 179(2): 72-80.
10. Kugiumtzis D. State space reconstruction parameters in the analysis of chaotic time series - the role of the time window length [J]. Physica: D, 1996, 95(1): 13-28.
11. Kim H S, Eykholt R J, Salas D. Nonlinear dynamics, delay times, and embedding windows [J]. Physica: D, 1999, 127(1): 48-60.
12. Otani M, Jones A. Automated embedding and creep phenomenon in chaotic time series [EB/OL]. http://www.cs.cf.ac.uk/ec/aecp.html, 2000-10-14/2003-05-15.
13. Stefansson A, Koncar N, Jones A J. A note on the gamma test [J]. Neural Computing and Applications 1999, 5(2): 131-133.
14. Kugiumtzis D, Lillekjendlie B, Christophersen N. Chaotic time series, part I: estimation of some invariant properties in state space [J]. Modeling Identification and Control, 1994, 15(4): 205-224.