Recurrence plots bridge deterministic systems and stochastic systems topologically and measure-theoretically
Yoshito Hirata1, Masanori Shiro2
1Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan.
Chaos (Woodbury, N.Y.)
|August 7, 2023
Summary
This study links recurrence triangles to the practical Detrended Fluctuation Analysis (DET) measure. Recurrence triangles offer theoretical support for DET and better identify stochasticity in time series data.
Area of Science:
- Nonlinear dynamics
- Time series analysis
- Complex systems
Background:
- Recurrence plots are crucial for analyzing complex systems.
- Recurrence triangles offer new insights into recurrence plot motifs.
- Detrended Fluctuation Analysis (DET) is a common metric for time series analysis.
Purpose of the Study:
- To connect conventional time series analysis values with recurrence triangles.
- To theoretically support the use of DET using recurrence triangles.
- To evaluate the efficacy of recurrence triangles in identifying system dynamics.
Main Methods:
- Quantifying recurrence plots using recurrence triangles.
- Utilizing topological and measure-theoretic values of recurrence triangles.
- Defining and calculating the typical recurrence triangle frequency dimension.
Main Results:
- The typical recurrence triangle frequency dimension fluctuates around 1 for deterministic chaos and exceeds 1 for stochastic systems.
- A strong correlation was found between the typical recurrence triangle frequency dimension and DET.
- Recurrence triangles provide theoretical grounding for the use of DET.
Conclusions:
- Recurrence triangles offer a robust method for quantifying time series properties.
- The study validates and enhances the application of DET in time series analysis.
- Recurrence triangles show consistent performance in distinguishing between deterministic and stochastic dynamics.
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