Analytical description of recurrence plots of dynamical systems with nontrivial recurrences

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

Research output: Contribution to journalArticle

7 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

Keywords

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

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