ANALYTICAL DESCRIPTION OF RECURRENCE PLOTS OF DYNAMICAL SYSTEMS WITH NONTRIVIAL RECURRENCES

  • ZOU Y
  • THIEL M
  • ROMANO M
 et al. 
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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 ε 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 ε to analyze experimental data by means of RPs.

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Authors

  • Y. ZOU

  • M. THIEL

  • M. C. ROMANO

  • J. KURTHS

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