| Title:
|
Determination of phase-space reconstruction parameters of chaotic time series (English) |
| Author:
|
Cai, Wei-Dong |
| Author:
|
Qin, Yi-Qing |
| Author:
|
Yang, Bing-Ru |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
44 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
557-570 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A new method called C-C-1 method is suggested, which can improve some drawbacks of the original C-C method. Based on the theory of period N, a new quantity S(t) for estimating the delay time window of a chaotic time series is given via direct computing a time-series quantity S(m,N,r,t), from which the delay time window can be found. The optimal delay time window is taken as the first period of the chaotic time series with a local minimum of S(t). Only the first local minimum of the average of a quantity Δ S2(t) is needed to ascertain the optimal delay time. The parameter of the C-C method - embedding dimension $m$ - is adjusted rationally. In the new method, the estimates of the optimal delay time and the optimal delay time window are more appropriate. The robustness of the C-C-1 method reaches 40 (English) |
| Keyword:
|
phase-space reconstruction |
| Keyword:
|
embedding window |
| Keyword:
|
delay time |
| Keyword:
|
time series |
| MSC:
|
37D45 |
| MSC:
|
37M10 |
| MSC:
|
62M10 |
| MSC:
|
62M15 |
| idZBL:
|
Zbl 1179.37048 |
| idMR:
|
MR2459073 |
| . |
| Date available:
|
2009-09-24T20:38:04Z |
| Last updated:
|
2012-06-06 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135874 |
| . |
| Reference:
|
[1] Grassberger P., Procaccia I.: Measure the strangeness of strange attractors.Physica D 9 (1983), 189–208 MR 0732572 |
| Reference:
|
[2] Huang R. S.: Chaos and Application.Wuhan University Press, Wuhan 2000 |
| Reference:
|
[3] Kim H. S., Eykholt, R., Salas J. D.: Nonlinear dynamics, delay times, and embedding windows.Physica D 127 (1999), 48–60 Zbl 0941.37054 |
| Reference:
|
[4] Lu J. H., Lu J. A., Chen S. H.: Analysis and Application of Chaotic Time Series.Wuhan University Press, Wuhan 2002 |
| Reference:
|
[6] Ma H. G., Li X. H., Wang G. H.: Selection of embedding dimension and delay time in phase space reconstruction.J. Xi’an Jiaotong University 38 (2004), 335–338 |
| Reference:
|
[7] Small M., Tse C. K.: Optimal embedding parameters: A modeling paradigm.Physica D: Nonlinear Phenomena 194 (2004), 283–296 MR 2075657 |
| Reference:
|
[9] Sauer T., Yorke J. A., Casdagli M.: Embedology.J. Statist. Phys. 65 (1991), 579–616 Zbl 0943.37506, MR 1137425 |
| Reference:
|
[10] Takens F.: Detecting Strange Attractors in Turbulence.Dynamical Systems and Turbulence. (Lecture Notes in Mathematics 898.) Springer-Verlag, Berlin 1981, pp. 366–381 Zbl 0513.58032, MR 0654900 |
| Reference:
|
[11] Takens F.: On the Numerical Determination of the Dimension of an Attractor.Dynamical System and Turbulence. (Lecture Notes in Mathematics 1125.) Springer-Verlag, Berlin 1985, pp. 99–106 Zbl 0561.58027, MR 0798084 |
| Reference:
|
[12] Wang Y., Xu W.: The methods and performance of phase space reconstruction for the time series in Lorenz system.J. Vibration Engrg. 19 (2006), 277–282 |
| Reference:
|
[13] Xiu C. B., Liu X. D., Zhang Y. H.: Selection of embedding dimension and delay time in the phase space reconstruction.Trans. Beijing Institute of Technology 23 (2003), 219–224 |
| Reference:
|
[14] Zhang Y., Ren C. L.: The methods to confirm the dimension of re-constructed phase space.J. National University of Defense Technology 27 (2005), 101–105 |
| . |
