Abstract
We have considered a permutation entropy method for analyzing chaotic, noisy, and chaotic noisy series. We have introduced the concept of permutation entropy from a survey of some features of information entropy (Shannon entropy), described the algorithm for its calculation, and indicated the advantages of this approach in the analysis of time series; the application of this method in the analysis of various model systems and experimental data has also been demonstrated.
Similar content being viewed by others
References
Nonlinear Analysis of Physiological Data, Ed. by H. Kantz (Springer, Berlin, 1996).
J.-P. Eckmann and D. Ruelle, Rev. Mod. Phys. 57, 617 (1985).
Ya. B. Pesin, Dimension Theory in Dynamical Systems (Univ. of Chicago Press, 1998).
P. Grassberger and I. Procaccia, Phys. Rev. A 28, 2591 (1983).
M. Ding, C. Grebogi, E. Ott, T. Sauer, and J. A. Yorke, Phys. Rev. Lett. 70, 3872 (1993).
H. D. I. Abarbanel, Analysis of Observed Chaotic Data (Springer, New York, 1996).
G. Bofetta, M. Cencini, M. Falcioni, and A. Vulpiani, Phys. Rep. 356, 367 (2002).
C. Bandt and B. Pompe, Phys. Rev. Lett. 88, 174102 (2002).
I. Veisi, N. Pariz, and A. Karimpour, in Proc. 7th IEEE Int. Conf. on Bioinformatics and Bioengineering, Boston, 2007, p.200.
K. Schindler, H. Gast, L. Stieglitz, A. Stibal, M. Hauf, R. Wiest, L. Mariani, and C. Rummel, Epilepsia 52, 1771 (2011).
C. Bian, C. Qin, Q. D. Y. Ma, and Q. Shen, Phys. Rev. E 85, 021906 (2012).
U. Parlitz, S. Berg, S. Luther, A. Schirdewan, J. Kurths, and N. Wessel, Comput. Biol. Med. 42, 319 (2012).
V. V. Kolesov and A. A. Potapov, Electromagn. Phenom. 5 (2), 89 (2005).
M. Zanin, Chaos 18, 013119 (2008).
L. Zunino, M. Zanin, B. M. Tabak, D. G. Perez, and O. A. Rosso, Phys. A 388, 2854 (2009).
C. E. Shannon, Bell Syst. Tech. J. 27, 379 (1948).
S. P. Kuznetsov, Dynamic Chaos (Fizmatlit, Moscow, 2001), pp. 43–63.
Yu. A. Kalinin, A. V. Starodubov, and N. N. Kuznetsov, Tech. Phys. 58, 923 (2013).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © S.A. Makarkin, A.V. Starodubov, Yu.A. Kalinin, 2017, published in Zhurnal Tekhnicheskoi Fiziki, 2017, Vol. 87, No. 11, pp. 1712–1717.
Rights and permissions
About this article
Cite this article
Makarkin, S.A., Starodubov, A.V. & Kalinin, Y.A. Application of permutation entropy method in the analysis of chaotic, noisy, and chaotic noisy series. Tech. Phys. 62, 1714–1719 (2017). https://doi.org/10.1134/S1063784217110202
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063784217110202