Nothing Special   »   [go: up one dir, main page]

Skip to main content
Log in

A historical review of recurrence plots

  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

In the last two decades recurrence plots (RPs)were introduced in many different scientific disciplines. It turned out how powerful this method is. After introducing approaches of quantification of RPs and by the study of relationships between RPs and fundamental properties of dynamical systems, this method attracted even more attention. After 20 years of RPs it is time to summarise this development in a historical context.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • C. Ahlstrom, P. Hult, P. Ask, Detection of the 3rd Heart Sound using Recurrence Time Statistics, Vol. 2 (2006), p. II1040

  • I. Aihara, S. Horai, H. Kitahata, K. Aihara, K. Yoshikawa, IEICE Trans. Fund. Electr. Comm. Comp. Sci. 90, 2154 (2007)

    Google Scholar 

  • V. Balakrishnan, G. Nicolis, C. Nicolis, Phys. Rev. E 61, 2490 (2000)

    Google Scholar 

  • M.C. Casdagli, Physica D 108, 12 (1997)

    Google Scholar 

  • T. Chelidze, V. De Rubeis, T. Matcharashvili, P. Tosi, Ann. Geophys. 49, 961 (2006)

    Google Scholar 

  • J. Chen, Y.-A. Li, D.-H. Wang, H. Gongcheng, D. Xuebao, J. Harbin, Eng. Univ. 27, 649 (2006)

    Google Scholar 

  • J.M. Choi, B.H. Bae, S.Y. Kim, Phys. Lett. A 263, 299 (1999)

    Google Scholar 

  • K.W. Church, J.I. Helfman, J. Comp. Graph. Stat. 2, 153 (1993)

    Google Scholar 

  • E. Domany, Physica A 288, 1 (2000)

  • J.-P. Eckmann, S.O. Kamphorst, D. Ruelle, Europhys. Lett. 5, 973 (1987)

    Google Scholar 

  • A.S. Elwakil, A.M. Soliman, Chaos, Solit. Fract. 10, 1399 (1999)

  • A. Facchini, H. Kantz, Phys. Rev. E 75, 036215 (2007)

    Google Scholar 

  • A. Facchini, H. Kantz, E. Tiezzi, Phys. Rev. E 72, 021915 (2005)

    Google Scholar 

  • A. Facchini, C. Mocenni, N. Marwan, A. Vicino, E. Tiezzi, Ecolog. Modell. 203, 339 (2007)

    Google Scholar 

  • P. Faure, H. Korn, Physica D 122, 265 (1998)

    Google Scholar 

  • J.B. Gao, H.Q. Cai, Phys. Lett. A 270, 75 (2000)

    Google Scholar 

  • C.G. Gilmore, J. Business Finance Account. 23, 1357 (1996)

  • A. Giuliani, R. Benigni, P. Sirabella, J.P. Zbilut, A. Colosimo, Biophys. J. 78, 136 (2000)

    Google Scholar 

  • A. Giuliani, R. Benigni, J.P. Zbilut, C.L. Webber Jr., P. Sirabella, A. Colosimo, Chem. Rev. 102, 1471 (2002)

    Google Scholar 

  • Google Inc. Australia, Google gDay, http://www.google.com.au/intl/en/gday/

  • A. Groth, Phys. Rev. E 72, 046220 (2005)

    Google Scholar 

  • S. Hermann, IEEE Trans. Inf. Technol. Biomed. 9, 392 (2005)

    Google Scholar 

  • M. Hirata, B. Saussol, S. Vaienti, Commun. Math. Phys. 206, 33 (1999)

    Google Scholar 

  • L. Holm, C. Sander, J. Molec. Biol. 233, 123 (1993)

    Google Scholar 

  • S. Horai, T. Yamada K. Aihara, IEEE Trans. Inst. Elect. Eng. Jpn. C 122, 141 (2002)

    Google Scholar 

  • M. Kac, Bull. Amer. Math. Soc. 53, 1002 (1947)

    Google Scholar 

  • A. Krishnan, A. Giuliani, J.P. Zbilut, M. Tomita, PLoS ONE 3, 2149 (2008)

    Google Scholar 

  • A. Krishnan, J.P. Zbilut, M. Tomita, A. Giuliani, Curr. Prot. Peptide Sci. 9, 28 (2008)

    Google Scholar 

  • G. Krishnan, R.K. Kaul, P. Jagadeeswaran, Nucl. Acids Res. 14, 543 (1986)

    Google Scholar 

  • J.B. Kruskal, Psychometr. 29, 1 (1964)

  • J.B. Kruskal, Time Warps, String Edits, and Macromolecules: The Theory and Practice of Sequence Comparison, edited by D. Sankoff, J.B. Kruskal (Addison-Wesley, Reading, Mass., 1983), p. 1

  • J. Kurths, U. Schwarz, C.P. Sonett, U. Parlitz, Nonlinear Proc. Geophys. 1, 72 (1994)

    Google Scholar 

  • Q. Li, Sol. Phys. 249, 135 (2008)

    Google Scholar 

  • G. Litak, T. Kamiński, J. Czarnigowski, D. Żbukowski, M. Wendeker, Meccanica 42, 423 (2007)

    Google Scholar 

  • E.N. Lorenz, J. Atmosph. Sci. 20, 120 (1963)

    Google Scholar 

  • P.C. Mahalanobis, Proc. Nation. Inst. Sci. 2, 49 (1936)

    Google Scholar 

  • T.K. March, S.C. Chapman, R.O. Dendy, Physica D 200, 171 (2005)

    Google Scholar 

  • N. Marwan, Untersuchung der Klimavariabilität in NW Argentinien mit Hilfe der quantitativen Analyse von Recurrence Plots, Master's thesis, Dresden University of Technology, Dresden University of Technology (1999)

  • N. Marwan, J. Kurths, Phys. Lett. A 302, 299 (2002)

    Google Scholar 

  • N. Marwan, J. Kurths, Phys. Lett. A 336, 349 (2005)

    Google Scholar 

  • N. Marwan, J. Kurths, P. Saparin, Phys. Lett. A 360, 545 (2007)

    Google Scholar 

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

    Google Scholar 

  • N. Marwan, M. Thiel, N.R. Nowaczyk, Nonl. Proc. Geophys. 9, 325 (2002)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  • M. Masugi, IEEE Trans. Circ. Syst. I: Fund. Theor. Appl. 53, 2318 (2006)

  • G. McGuire, N.B. Azar, M. Shelhamer, Phys. Lett. A 237, 43 (1997)

    Google Scholar 

  • G.M. Mindlin, R. Gilmore, Physica D 58, 229 (1992)

    Google Scholar 

  • E.J. Ngamga, A. Nandi, R. Ramaswamy, M.C. Romano, M. Thiel, J. Kurths, Phys. Rev. E 75, 036222 (2007)

    Google Scholar 

  • J. Ningde, Z. Guibo, D. Fang, C. Wanpeng, Lect. Notes Comp. Sci. 4223, 1213 (2006)

    Google Scholar 

  • H. Poincaré, Acta Math. 13, 1 (1890)

    Google Scholar 

  • I. Procaccia, S. Thomae, C. Tresser, Phys. Rev. A 35, 1884 (1987)

    Google Scholar 

  • A. Provenzale, L.A. Smith, R. Vio, G. Murante, Physica D 58, 31 (1992)

    Google Scholar 

  • G.K. Rohde, J.M. Nichols, B.M. Dissinger, F. Bucholtz, Physica D 237, 619 (2008)

    Google Scholar 

  • M.C. Romano, M. Thiel, J. Kurths, AIP Conf. Proc. 742, 330 (2004)

    Google Scholar 

  • M.C. Romano, M. Thiel, J. Kurths, C. Grebogi, Phys. Rev. E 76, 036211 (2007)

    Google Scholar 

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

    Google Scholar 

  • M.C. Romano, M. Thiel, J. Kurths, W. von Bloh, Phys. Lett. A 330, 214 (2004)

    Google Scholar 

  • M. Rustici, C. Caravati, E. Petretto, M. Branca, N. Marchettini, J. Phys. Chem. A 103, 6564 (1999)

    Google Scholar 

  • H. Sakoe, S. Chiba, IEEE Trans. Acoust., Speech, Sign. Proc. 26, 43 (1978)

    Google Scholar 

  • S. Schinkel, N. Marwan, J. Kurths, Cognitive Neurodyn. 1, 317 (2007)

  • A.K. Sen, R. Longwic, G. Litak, K. Górski, Mech. Syst. Sign. Proc. 22, 362 (2008)

    Google Scholar 

  • M. Thiel, M.C. Romano, J. Kurths, Appl. Nonl. Dyn. 11, 20 (2003)

    Google Scholar 

  • M. Thiel, M.C. Romano, J. Kurths, Phys. Lett. A 330, 343 (2004)

    Google Scholar 

  • M. Thiel, M.C. Romano, J. Kurths, Nonl. Dyn. 44, 299 (2006)

    Google Scholar 

  • M. Thiel, M.C. Romano, J. Kurths, R. Meucci, E. Allaria, F.T. Arecchi, Physica D 171, 138 (2002)

    Google Scholar 

  • M. Thiel, M.C. Romano, J. Kurths, M. Rolfs, R. Kliegl, Phil. Trans. Royal Soc. A 366, 545 (2008)

    Google Scholar 

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

    Google Scholar 

  • L.L. Thurstone, Psychol. Rev. 34, 273 (1927)

    Google Scholar 

  • L.L. Trulla, A. Giuliani, J.P. Zbilut, C.L. Webber Jr., Phys. Lett. A 223, 255 (1996)

    Google Scholar 

  • T. Živković, K. Rypdal, Phys. Rev. E 77, 037401 (2008)

    Google Scholar 

  • D. Vretenar, N. Paar, P. Ring, G.A. Lalazissis, Phys. Rev. E 60, 308 (1999)

    Google Scholar 

  • C.L. Webber Jr., A. Giuliani, J.P. Zbilut, A. Colosimo, Proteins: Struct. Funct. Genet. 44, 292 (2001)

    Google Scholar 

  • C.L. Webber Jr., J.P. Zbilut, J. Appl. Phys. 76, 965 (1994)

    Google Scholar 

  • J.-M. Zaldívar, F. Strozzi, S. Dueri, D. Marinov, J.P. Zbilut, Ecolog. Modell. 210, 58 (2008)

    Google Scholar 

  • J.P. Zbilut, A. Giuliani, C.L. Webber Jr., Phys. Lett. A 267, 174 (2000)

    Google Scholar 

  • J.P. Zbilut, A. Giuliani, C.L. Webber Jr., Phys. Lett. A 246, 122 (1998)

    Google Scholar 

  • J.P. Zbilut, M. Koebbe, H. Loeb, G. Mayer-Kress, Proceedings of the IEEE Conference on Computers in Cardiology, Chicago, 1990 (IEEE Comp. Soc. Press, 1990), p. 263

  • J.P. Zbilut, J.C. Mitchell, A. Giuliani, N. Marwan, C.L. Webber Jr., Physica A 343, 348 (2004)

  • J.P. Zbilut, C.L. Webber Jr., Phys. Lett. A 171, 199 (1992)

    Google Scholar 

  • J.P. Zbilut, C.L. Webber Jr., Int. J. Bifurc. Chaos 17, 3477 (2007)

    Google Scholar 

  • N.V. Zolotova, D.I. Ponyavin, Astron. Astrophys. 449, L1 (2006)

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

    Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to N. Marwan.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Marwan, N. A historical review of recurrence plots. Eur. Phys. J. Spec. Top. 164, 3–12 (2008). https://doi.org/10.1140/epjst/e2008-00829-1

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2008-00829-1

Keywords

Navigation