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Recurrence plots and unstable periodic orbits.

Elizabeth Bradley1, Ricardo Mantilla

  • 1Department of Computer Science, University of Colorado, Boulder, Colorado 80309-0430.

Chaos (Woodbury, N.Y.)
|June 5, 2003
PubMed
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Recurrence plots visualize sequential data correlations. This study proposes using unstable periodic orbits within chaotic attractors to interpret recurrence plot geometry, aiding dynamical system identification.

Area of Science:

  • Dynamical Systems and Chaos Theory
  • Data Visualization
  • Nonlinear Time Series Analysis

Background:

  • Recurrence plots (RPs) offer a 2D visualization for sequential data, revealing correlations across scales.
  • The complex geometric structure of RPs can pose challenges for interpretation.
  • Understanding the underlying dynamics of chaotic systems is crucial for accurate analysis.

Purpose of the Study:

  • To propose unstable periodic orbits (UPOs) as a basis set for interpreting the geometry of recurrence plots.
  • To develop a method for locating UPOs within chaotic time-series data using RPs.
  • To enhance the utility of recurrence plots for identifying dynamical systems.

Main Methods:

  • Utilizing recurrence plots (RPs) as a visualization technique for sequential data.

Related Experiment Videos

  • Employing the concept of unstable periodic orbits (UPOs) embedded within chaotic attractors.
  • Analyzing the geometric structure of recurrence plots in relation to UPOs.

    • Main Results:

    • Demonstrated that UPOs provide a meaningful basis set for understanding RP geometry.
    • Developed a method to locate UPOs directly from chaotic time-series data via RPs.
    • Showcased the potential of RPs, when interpreted through UPOs, for dynamical system identification.

    Conclusions:

    • Unstable periodic orbits offer a powerful framework for interpreting recurrence plot geometry.
    • This approach simplifies the location of UPOs in chaotic time-series data.
    • Recurrence plots, when analyzed with UPOs, present a promising tool for dynamical system identification.