Recurrence analysis of quasiperiodicity in experimental fluid data

The European Physical Journal Special Topics volume 164, pages 23–33 (2008)Cite this article

Abstract

We propose a procedure to analyze experimental data which exhibit different dynamical regimes, namely, periodicity, chaoticity and quasiperiodicity by means of Recurrence Plots (RPs). We show that, based on the recurrence properties captured by RPs, we are able to characterize successfully the type of dynamics. This approach is particularly useful for detecting the existence of quasiperiodic motion in short time series. We show the capability and validity of this method by analyzing time series from fluid experiments.

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References

  1. A. Katok, B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems (Cambridge University Press, 1995)

  2. J.-P. Eckmann, S.O. Kamphorst, D. Ruelle, Europhys. Lett. 4, 973 (1987)

    Google Scholar 

  3. J.P. Zbilut, N. Thomasson, C.L. Webber, Med. Eng. Phys. 24, 53 (2002)

    Google Scholar 

  4. N. Marwan, N. Wessel, U. Meyerfeldt, A. Schirdewan, J. Kurths, Phys. Rev. E 66, 026702 (2002)

    Google Scholar 

  5. N. Marwan, M.C. Romano, M. Thiel, J. Kurths, Phys. Rep. 438, 237 (2007)

    Google Scholar 

  6. N. Thomasson, T.J. Hoeppner, C.L. Webber, J.P. Zbilut, Phys. Lett. A 279, 94 (2001)

    Google Scholar 

  7. H. Castellini, L. Romanelli, Physica A 342, 301 (2004)

    Google Scholar 

  8. N. Marwan, M.H. Trauth, M. Vuille, J. Kurths, Climate Dyn. 21, 317 (2003)

    Google Scholar 

  9. M.C. Romano, M. Thiel, J. Kurths, I.Z. Kiss, J. Hudson, Europhys. Lett. 71, 466 (2005)

    Google Scholar 

  10. M. Thiel, M.C. Romano, J. Kurths, M. Rolfs, R. Kliegl, Europhys. Lett. 75, 535 (2006)

    Google Scholar 

  11. J. Kurths, M.C. Romano, M. Thiel, G.V. Osipov, M.V. Ivanchenko, I.Z. Kiss, J.L. Hudson, Nonlinear Dyn. 44, 135 (2006)

    Google Scholar 

  12. N.B. Slater, Proc. Cambridge Philos. Soc. 63, 1115 (1967)

    Google Scholar 

  13. D.H. Mayer, Lett. Math. Phys. 16, 139 (1988)

    Google Scholar 

  14. M. Theunissen, C. Nicolis, G. Nicolis, J. Statis. Phys. 94, 437 (1999)

    Google Scholar 

  15. N. Buric, A. Rampioni, G. Turchetti, Chaos, Solit. Fract. 23, 1829 (2005)

    Google Scholar 

  16. Y. Zou, D. Pazó, M.C. Romano, M. Thiel, J. Kurths, Phys. Rev. E 76, 016210 (2007)

    Google Scholar 

  17. P.L. Read, M.J. Bel, D.W. Johnson, R.M. Small, J. Fluid Mech. 238, 599 (1992)

    Google Scholar 

  18. A. Randriamampianina, W.-G. Früh, P.L. Read, P. Maubert, J. Fluid Mech. 561, 359 (2006)

    Google Scholar 

  19. M. Thiel, M.C. Romano, P. Read, J. Kurths, Chaos 14, 234 (2004)

    Google Scholar 

  20. J. Theiler, Phys. Rev. A 34, 2427 (1986)

    Google Scholar 

  21. H.D.I. Abarbanel, R. Brown, J. Sidorowich, L. Tsimring, Rev. Mod. Phys. 65, 1331 (1993)

    Google Scholar 

  22. R. Hegger, H. Kantz, T. Schreiber, Chaos 9, 413 (1999)

    Google Scholar 

  23. H. Kantz, T. Schreiber, Nonlinear Time Series Analysis, 2nd edn. (Cambridge University Press, Cambridge, 2004)

  24. J. Kurths, H. Herzel, Physica D 25, 165 (1987)

    Google Scholar 

  25. Y. Zou, M. Thiel, M.C. Romano, J. Kurths, Chaos 17, 043101 (2007)

    Google Scholar 

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Affiliations

  1. Potsdam Institute for Climate Impact Research, PO Box 601203, 14412, Potsdam, Germany

    Y. Zou & J. Kurths

  2. Nonlinear Dynamics Group, University of Potsdam, Am Neuen Palais 10, 14469, Potsdam, Germany

    Y. Zou & J. Kurths

  3. Department of Physics, University of Aberdeen, Aberdeen AB 24 3, UE, UK

    M. Thiel & M.C. Romano

  4. Atmospheric, Oceanic and Planetary Physics, Clarendon Laboratory, Parks Road, Oxford, OX1 3PU, UK

    P.L. Read

  5. Institut für Physik, Humboldt Universität zu Berlin, Newtonstr. 15, 12489, Berlin, Germany

    J. Kurths

Authors
  1. Y. Zou
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  2. M. Thiel
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  3. M.C. Romano
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  4. P.L. Read
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  5. J. Kurths
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Correspondence to Y. Zou.

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Zou, Y., Thiel, M., Romano, M. et al. Recurrence analysis of quasiperiodicity in experimental fluid data. Eur. Phys. J. Spec. Top. 164, 23–33 (2008). https://doi.org/10.1140/epjst/e2008-00831-7

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Keywords

  • Lyapunov Exponent
  • European Physical Journal Special Topic
  • Return Time
  • Recurrence Interval
  • Recurrence Plot