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Ordinal patterns in the Duffing oscillator: Analyzing powers of characterization.
Ivan Gunther1, Arjendu K Pattanayak1, Andrés Aragoneses2
1Department of Physics and Astronomy, Carleton College, 1 N College St, Northfield, Minnesota 55057, USA.
Chaos (Woodbury, N.Y.)
|March 3, 2021
Summary
Ordinal patterns, a time-series analysis tool, reveal dynamical symmetry changes invisible to permutation entropy. This method offers novel predictive capabilities for system stability.
Area of Science:
- Nonlinear dynamics
- Time-series analysis
- Chaos theory
Background:
- Ordinal patterns are a preliminary step for calculating permutation entropy.
- Permutation entropy and Lyapunov exponents characterize system dynamics.
- Ordinal patterns contain more information than permutation entropy or Lyapunov exponents.
Purpose of the Study:
- To demonstrate that ordinal patterns capture dynamical symmetry changes missed by other measures.
- To investigate the relationship between symmetry changes and system stability using the Duffing oscillator.
Main Methods:
- Analysis of time-series data from the Duffing oscillator.
- Application of ordinal pattern analysis.
- Comparison with permutation entropy and Lyapunov exponents.
Main Results:
- Ordinal patterns detected changes in dynamical symmetry in the Duffing oscillator.
- These symmetry changes were not discernible through permutation entropy.
- Observed correlations between symmetry changes and neighboring parameter stability.
Conclusions:
- Ordinal pattern analysis provides deeper insights into system dynamics than permutation entropy.
- Changes in dynamical symmetry detected by ordinal patterns may predict changes in system stability.
- This technique offers a novel approach for analyzing complex systems.
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