Advertisement

The European Physical Journal Special Topics

, Volume 164, Issue 1, pp 23–33 | Cite as

Recurrence analysis of quasiperiodicity in experimental fluid data

  • Y. ZouEmail author
  • M. Thiel
  • M.C. Romano
  • P.L. Read
  • J. Kurths
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.

Keywords

Lyapunov Exponent European Physical Journal Special Topic Return Time Recurrence Interval Recurrence Plot 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

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

Copyright information

© EDP Sciences and Springer 2008

Authors and Affiliations

  • Y. Zou
    • 1
    • 2
    Email author
  • M. Thiel
    • 3
  • M.C. Romano
    • 3
  • P.L. Read
    • 4
  • J. Kurths
    • 1
    • 2
    • 5
  1. 1.Potsdam Institute for Climate Impact ResearchPotsdamGermany
  2. 2.Nonlinear Dynamics Group, University of PotsdamPotsdamGermany
  3. 3.Department of PhysicsUniversity of AberdeenUEUK
  4. 4.Atmospheric, Oceanic and Planetary Physics, Clarendon LaboratoryOxfordUK
  5. 5.Institut für Physik, Humboldt Universität zu BerlinBerlinGermany

Personalised recommendations