Analytical description of recurrence plots of dynamical systems with nontrivial recurrences

Y. Zou, Marco Thiel, M Carmen Romano , Jurgen Kurths

Research output: Contribution to journal › Article

6 Citations (Scopus)

Abstract

In this paper we study recurrence plots (RPs) for the simplest example of nontrivial recurrences, namely in the case of a quasiperiodic motion. This case can be still studied analytically and constitutes a link between simple periodic and more complicated chaotic dynamics. Since we deal with nontrivial recurrences, the size of the neighborhood ¿ to which the trajectory must recur, is larger than zero. This leads to a nonzero width of the lines, which we determine analytically for both periodic and quasiperiodic motion. The understanding of such microscopic structures is important for choosing an appropriate threshold ¿ to analyze experimental data by means of RPs.
Original languageEnglish
Pages (from-to)4273-4283
Number of pages11
JournalInternational Journal of Bifurcation and Chaos
Volume17
Issue number12
DOIs
Publication statusPublished - Dec 2007

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Recurrence Plot
Quasi-periodic Motion
Recurrence
Dynamical systems
Dynamical system
Trajectories
Periodic Motion
Chaotic Dynamics
Experimental Data
Trajectory
Line
Zero

Keywords

  • recurrence plot
  • analytic description
  • quasiperiodic motion
  • nontrivial recurrence

Cite this

Analytical description of recurrence plots of dynamical systems with nontrivial recurrences. / Zou, Y.; Thiel, Marco; Romano , M Carmen; Kurths, Jurgen.

In: International Journal of Bifurcation and Chaos, Vol. 17, No. 12, 12.2007, p. 4273-4283.

Research output: Contribution to journal › Article

Zou, Y, Thiel, M, Romano , MC & Kurths, J 2007, 'Analytical description of recurrence plots of dynamical systems with nontrivial recurrences', International Journal of Bifurcation and Chaos, vol. 17, no. 12, pp. 4273-4283. https://doi.org/10.1142/S0218127407019949
Zou Y, Thiel M, Romano MC, Kurths J. Analytical description of recurrence plots of dynamical systems with nontrivial recurrences. International Journal of Bifurcation and Chaos. 2007 Dec;17(12):4273-4283. https://doi.org/10.1142/S0218127407019949
Zou, Y. ; Thiel, Marco ; Romano , M Carmen ; Kurths, Jurgen. / Analytical description of recurrence plots of dynamical systems with nontrivial recurrences. In: International Journal of Bifurcation and Chaos. 2007 ; Vol. 17, No. 12. pp. 4273-4283.
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