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Estimating the Shannon entropy: recurrence plots versus symbolic dynamics
1CORIA UMR 6614 - Université de Rouen, Avenue de l'Université, Boîte Postale 12, F-76801 Saint-Etienne du Rouvray cedex, France.
Physical Review Letters
|August 16, 2006
Summary
This study introduces a new Shannon entropy definition using recurrence plots to accurately measure chaotic dynamics. The new measure correlates with the largest Lyapunov exponent, aligning with the Pesin conjecture.
Area of Science:
- Nonlinear dynamics
- Chaos theory
- Statistical analysis
Background:
- Recurrence plots (RPs) quantify chaotic dynamics.
- Recurrence Quantification Analysis (RQA) transforms RPs into statistical measures.
- Previous RQA Shannon entropy correlated inversely with the largest Lyapunov exponent, contradicting expectations.
Purpose of the Study:
- To resolve the discrepancy in Shannon entropy interpretation within RQA.
- To introduce a new Shannon entropy definition based on RPs.
- To verify the new definition's correlation with the largest Lyapunov exponent, supporting the Pesin conjecture.
Main Methods:
- Utilizing recurrence plots for dynamical system analysis.
- Developing a novel Shannon entropy calculation from recurrence plot properties.
- Comparing the new Shannon entropy with traditional symbolic dynamics approaches.
Main Results:
- The newly defined Shannon entropy shows a direct correlation with the largest Lyapunov exponent.
- This finding supports the Pesin conjecture, which relates entropy to Lyapunov exponents.
- The study provides a more consistent interpretation of entropy in chaotic systems.
Conclusions:
- The novel Shannon entropy definition accurately reflects chaotic dynamics.
- This work reconciles RQA measures with established chaos theory predictions.
- The findings offer a refined tool for analyzing complex systems.
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