Usefulness Study of Rosenstein and Eckmann Procedures for Identification of Chaotic Time Series

Authors

  • D. Hallmann Akademia Morska w Gdyni, Morska 81-87, 81–225 Gdynia, Wydział Elektryczny, Katedra Elektroenergetyki Okrętowej
  • P. Jankowski Akademia Morska w Gdyni, Morska 81-87, 81–225 Gdynia, Wydział Elektryczny, Katedra Elektroenergetyki Okrętowej

DOI:

https://doi.org/10.26408.103.09

Keywords:

chaos, time series, Lyapunov exponent

Abstract

This paper presents the results of simulation tests using the Eckmann and Rosenstein procedures for calculating Lyapunov exponents based on a time series. For verifying and evaluating the suitability of these procedures as a reference time series, points generated by logistic mapping for which the trajectory of Lyapunov's coefficients is known was applied.

References

Baker, G.L., Gollub, J.P., 1998, Wstęp do dynamiki układów chaotycznych, Wydawnictwo Naukowe PWN, Warszawa.

[2] Eckmann, J.P., Kamphorst, S.O., Ruelle, D., Ciliberto, S., 1986, Liapunov exponents from time series, Physical Review A, vol. 34, no. 6, s. 4971–4979.

[3] Kantz, H., 1994, A Robust Method to Estimate the Maximal Lyapunov Exponent of a Time Series, Physical Letters A, vol. 185(1), s. 77–87.

[4] Kantz, H., Schreiber, T., 2004, Nonlinear Time Series Analysis, Cambridge University Press, Cambridge.

[5] Kennel, M.B., Brown, R., Abarbanel, H.D.I., 1992, Detecting Embedding Dimension for Phase Space Reconstruction Using a Geometrical Construction, Physical Review A, vol. 45.

[6] Largest Lyapunov Exponent with Rosenstein’s Algorithm, http://www.mathworks.com/matlabcentral/ fileexchange/38424-largest-lyapunov-exponent-with-rosenstein-s-algorithm.

[7] Packard, N.H., Crutchfield, J.P, Farmer, J.D, Shaw R.S., 1980, Geometry from a time series, Physical Review letters, vol. 45, no. 9, s. 712–716.

[8] Peitgen, H., Jürgens, H., Saupe, D., 1996, Granice chaosu. Fraktale, Wydawnictwo Naukowe PWN, Warszawa.

[9] Peters, E.E., 1997, Teoria chaosu a rynki kapitałowe, WiG_Press, Warszawa.

[10] Rosenstein, T., Collins, J.J., De Luca, C.J., 1993, A practical method for calculating largest Lyapunov exponents from small data sets, Physica D: Nonlinear Phenomena, vol. 65, no. 1, s. 117–134.

[11] Schuster, H.G., 1995, Chaos deterministyczny, Wydawnictwo Naukowe PWN, Warszawa.

[12] Shapour, M., 2017, LYAPROSEN: MATLAB function to calculate Lyapunov exponent, https://ideas.repec.org/c/boc/bocode/t741502.html.

[13] Wolf, A., Swift, J., Swinney, H., Vastano, J., 1985, Determining Lyapunov Exponents from a Time Series, Physica D, vol. 16, s. 285–317.

Published

2018-12-31

How to Cite

Hallmann, D., & Jankowski, P. (2018). Usefulness Study of Rosenstein and Eckmann Procedures for Identification of Chaotic Time Series. Scientific Journal of Gdynia Maritime University, (103), 120–136. https://doi.org/10.26408.103.09

Issue

Section

Articles