Recurrence threshold selection for obtaining robust recurrence characteristics in different embedding dimensions.

Area of Science:

• Dynamical systems analysis
• Nonlinear time series analysis
• Complex systems science

Background:

• Recurrence quantification analysis (RQA) is widely used to study dynamical systems.
• Choosing appropriate recurrence thresholds is critical for accurate RQA results.
• Current threshold selection methods can be sensitive to system parameters like embedding dimension.

Purpose of the Study:

• To investigate the distribution of pairwise distances between state vectors in reconstructed state spaces.
• To propose a novel method for selecting recurrence thresholds based on this distribution.
• To evaluate the impact of the proposed method on RQA results and their dependence on embedding dimension.

Main Methods:

• Time-delay embedding for state space reconstruction.
• Empirical analysis of pairwise distance distributions.
• Calculation of recurrence plots using thresholding based on fixed percentiles of the distance distribution.
• Comparison with commonly used threshold selection methods.

Main Results:

• The shape of the pairwise distance distribution changes with increasing embedding dimension.
• Selecting the recurrence threshold based on a fixed percentile of the distance distribution.
• This percentile-based method reduces the dependence of RQA measures on the embedding dimension.
• Numerical validation on model systems with time-dependent parameters.

Conclusions:

• The pairwise distance distribution provides key insights for recurrence threshold selection.
• A percentile-based thresholding strategy offers a more robust approach to RQA.
• This method enhances the reliability of recurrence quantification analysis across different embedding dimensions.