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Summary

This study introduces new symbolic recurrence measures to quantify dynamic structures without needing a distance parameter. These methods effectively analyze complex system behaviors like transient dynamics and bifurcations.

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Area of Science:

  • Nonlinear dynamics
  • Time series analysis
  • Recurrence quantification analysis

Background:

  • Traditional recurrence quantification analysis often relies on a distance parameter, which can be difficult to set optimally.
  • Understanding complex dynamic systems requires robust methods for quantifying structural changes and transient behaviors.

Purpose of the Study:

  • To introduce novel symbolic recurrence plots and invariant measures that are independent of the distance parameter.
  • To provide a tool for quantifying dynamic structures in complex systems.
  • To enable the study of transient behavior, coexistence of attractors, bifurcations, and structural changes.

Main Methods:

  • Development of symbolic recurrence plots based on the concept of symbolic correlation integral.
  • Introduction of associated invariant measures that are parameter-free.
  • Empirical application to electrocardiography (ECG) data.

Main Results:

  • The proposed symbolic recurrence measures are independent of the distance parameter, simplifying their application.
  • These measures successfully quantify dynamic structures and allow for the analysis of complex phenomena.
  • Demonstrated utility in analyzing real-world data, such as electrocardiography.

Conclusions:

  • Symbolic recurrence measures offer a robust and parameter-free approach to quantifying dynamic structures.
  • These methods enhance the study of complex system dynamics, including transient behaviors and bifurcations.
  • The approach is validated through its application to physiological time series data.