Abstract
The state space reconstruction is the major important quantitative index for describing non-linear 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
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.
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.
Berndt Pilgram, Kaplan Daniel T. A comparison of estimators for 1/f noise[J].Phys D, 1998,114(3):108–122.
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.
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.
Badii R, Broggi G, Derighetti B, et al. Dimension increase in filtered chaotic signals[J].Phys Rev Lett, 1988,60(4):979–984.
Mitschke F. A causal filters for chaotic signals[J].Phys Rev A, 1990,41:1169–1171.
Scargle J D. Studies in astronomical time series analysis IV, Modeling chaotic and random processes with linear filters[J].Astrophys J, 1990,359(12):469–482.
Broomherd D S. Extracting qualitatire dynamics from experimental data[J].Phys. D, 1987,20 (11):217–236.
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.
Liebert W, Pawalzik K, Schuster H G. Optimal embeddings of chaotic attractors from topological considerations[J].Europ Physics Lett, 1991,15(1):521–526.
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 Mechanica Sinica, 1989,15(1):82–92.
MA Jun-hai. The non-linear dynamic system reconstruction of the chaotic time series[D]. a thesis for Degree of engineering. Tianjin: Tianjin University, 1997. (in Chinese).
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.
Theiler J. Statistical precision of dimension estimators[J].Phys Rev A, 1990,41(6):3038–3051.
Author information
Authors and Affiliations
Additional information
Paper from CCHEN Yu-shu, Member of Editorial Committee, AMM
Foundation item: the National Natural Science Foundation of China(1990510)
Biographies: MA Jun-hai (1965-) CCHEN Yu-shu(1931-)
Rights and permissions
About this article
Cite this article
Jun-hai, M., Yu-shu, C. An analytic and application to state space reconstruction about chaotic time series. Appl Math Mech 21, 1237–1245 (2000). https://doi.org/10.1007/BF02459244
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02459244