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Updated: Jun 6, 2025
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Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography
Published on: June 15, 2018
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Complexity measure of extreme events
Dhiman Das1, Arnob Ray1,2, Chittaranjan Hens3
1Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India.
Chaos (Woodbury, N.Y.)
|December 2, 2024
Summary
This study introduces a new method to measure the complexity of extreme events in chaotic signals. The findings show this complexity measure can distinguish extreme chaos from non-extreme chaos.
Area of Science:
- Nonlinear dynamics
- Signal processing
- Complexity science
Background:
- Complexity measures are crucial for characterizing irregular signals.
- Existing methods often focus on general chaos, neglecting extreme event complexity.
- A gap exists in quantifying and distinguishing extreme chaotic events.
Purpose of the Study:
- To quantify and compare the complexity of extreme events versus non-extreme chaotic signals.
- To develop a method capable of distinguishing between these two signal types.
- To explore the transition dynamics leading to extreme events.
Main Methods:
- Utilizing normalized Shannon entropy combined with disequilibrium.
- Analyzing signal complexity across different system parameters.
- Employing three distinct dynamical systems: Liénard system, Ikeda map, and Hindmarsh-Rose system.
Main Results:
- The combined entropy and disequilibrium measure successfully distinguishes extreme from non-extreme chaos.
- The method identifies transition points, including Pomeau-Manneville intermittency and interior crisis.
- A general complexity trend shows an increase, peak, and subsequent decrease during transitions to extreme events.
Conclusions:
- The proposed complexity measure is effective for differentiating extreme chaotic events.
- This approach provides insights into the dynamics of signal transitions towards extreme behavior.
- The findings are validated across multiple complex dynamical systems.
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