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Ordinal patterns for characterization of transition to extreme events
S Leo Kingston1,2, Tomasz Kapitaniak3, Aditi Kathpalia4
1Center for Nonlinear and Complex Networks, SRM Institute of Science and Technology, Ramapuram, Chennai 600 089, India.
Chaos (Woodbury, N.Y.)
|May 29, 2026
Summary
Ordinal patterns, using permutation entropy, effectively distinguish extreme events from normal dynamics in complex systems. This method surpasses traditional techniques like the largest Lyapunov exponent for analyzing nonlinear data.
Area of Science:
- Nonlinear Dynamics and Complex Systems Science
- Information Theory and Data Analysis
Background:
- Ordinal patterns offer a symbolic representation for analyzing complex nonlinear dynamical systems and real-world data.
- Understanding extreme events in these systems is crucial for prediction and mitigation.
Purpose of the Study:
- To evaluate the effectiveness of ordinal pattern measures in characterizing extreme events across different dynamical processes.
- To compare ordinal pattern analysis with traditional methods like the largest Lyapunov exponent for extreme event detection.
Main Methods:
- Application of ordinal pattern-based permutation entropy to analyze three types of large expansions: strange nonchaotic, chaotic, and hyperchaotic extreme events.
- Validation of the method's robustness using noise-induced extreme events.
- Comparison with the largest Lyapunov exponent method.
Main Results:
- Permutation entropy successfully distinguishes between extreme and non-extreme events across diverse dynamic processes.
- The largest Lyapunov exponent method failed to show unique features for different extreme event types.
- Ordinal pattern measures demonstrated robustness even with noise-induced extreme events.
Conclusions:
- Ordinal pattern measures, particularly permutation entropy, are effective tools for uncovering the complexity of extreme events in nonlinear systems.
- This approach provides a more sensitive method for characterizing extreme events compared to the largest Lyapunov exponent.
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