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Study of system dynamics through recurrence analysis of regular windows
1Faculty of Mechanical Engineering, Lublin University of Technology, Nadbystrzycka 36, 20-618 Lublin, Poland.
Chaos (Woodbury, N.Y.)
|October 31, 2021
Summary
Selecting the threshold parameter (ɛ) in recurrence quantification analysis is crucial. This study introduces a novel procedure using variability and convergence criteria to determine optimal ɛ values for dynamical system analysis.
Area of Science:
- Dynamical Systems Analysis
- Nonlinear Time Series Analysis
- Recurrence Quantification Analysis (RQA)
Background:
- Recurrence quantification analysis (RQA) is sensitive to parameter choices, impacting interpretation of dynamical system behavior.
- While embedding parameters are well-defined, optimal selection rules for the threshold parameter (ɛ) remain an active research area.
- Inconsistent parameter selection can lead to unreliable recurrence measures and flawed dynamical system characterization.
Purpose of the Study:
- To propose a systematic procedure for selecting the threshold parameter (ɛ) in RQA.
- To establish criteria for determining optimal point density in vector series for RQA.
- To enhance the reliability and reproducibility of RQA in dynamical system studies.
Main Methods:
- Development of a procedure for selecting ɛ and point density based on variability criteria.
- Application of convergence criteria to identify suitable parameter ranges for RQA.
- Utilizing a linear convergence criterion for recurrence results to narrow down optimal ɛ values.
Main Results:
- A robust method for determining appropriate threshold parameter (ɛ) values is presented.
- The proposed procedure effectively identifies suitable point densities for vector series analysis.
- A narrow, suitable range for the ɛ parameter is identified through linear convergence analysis.
Conclusions:
- The developed procedure offers a reliable approach to parameter selection in RQA.
- This method improves the accuracy and consistency of dynamical system analysis using RQA.
- The findings contribute to establishing standardized practices for RQA parameter determination.
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