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A bottom-up approach for recurrence detection based on sampling distance.

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This study introduces a new method for recurrence analysis in dynamical systems using a variable threshold based on sampling distance. This approach stabilizes recurrence structures and effectively mitigates tangential motion effects, improving data analysis.

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Area of Science:

  • Dynamical Systems Analysis
  • Nonlinear Dynamics
  • Time Series Analysis

Background:

  • Recurrence analysis of dynamical systems is challenged by tangential motion effects.
  • Threshold selection is critical, especially for non-stationary data.
  • Existing methods struggle with abrupt transitions and noise.

Purpose of the Study:

  • To introduce a novel, robust thresholding method for recurrence analysis.
  • To mitigate the tangential motion effect in recurrence quantification.
  • To enhance the analysis of non-stationary and noisy dynamical systems.

Main Methods:

  • Utilizing the distance between successive phase space points as a recurrence threshold reference.
  • Developing a bottom-up thresholding approach.
  • Normalizing the method for sampling frequency independence.

Main Results:

  • The proposed method yields stable recurrence structures, outperforming previous techniques.
  • It effectively handles abrupt transitions in dynamical systems.
  • The method demonstrates noise resistance and independence from sampling frequency.

Conclusions:

  • The sampling distance-based thresholding method offers a stable and reliable approach to recurrence analysis.
  • It provides a clear reference for avoiding tangential motion effects.
  • This technique enhances the quantification and interpretation of dynamical system behavior, particularly for non-stationary data.