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Characterizing Complex Dynamics in the Classical and Semi-Classical Duffing Oscillator Using Ordinal Patterns
Max L Trostel1, Moses Z R Misplon1, Andrés Aragoneses1
1Department of Physics and Astronomy, Carleton College, Northfield, MN 55057, USA.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
We analyzed the complex dynamics of the driven double-well Duffing oscillator using ordinal pattern analysis. This method reveals hidden dynamical regimes within chaos, offering new insights into classical-to-quantum transitions.
Area of Science:
- Nonlinear Dynamics
- Chaos Theory
- Quantum Mechanics
Background:
- The driven double-well Duffing oscillator is a fundamental model exhibiting complex dynamics, including chaos.
- It is relevant for understanding the transition from classical to quantum chaos.
- Traditional statistical tools have limitations in characterizing all dynamical regimes.
Purpose of the Study:
- To explore the complexity of Duffing oscillator dynamics in classical and semi-classical regimes.
- To apply ordinal pattern analysis for a deeper understanding of chaotic behavior.
- To identify novel dynamical regimes not detectable by conventional methods.
Main Methods:
- Utilized ordinal pattern analysis to probe system dynamics.
- Investigated the driven double-well Duffing oscillator across classical and semi-classical regimes.
- Analyzed hierarchies and probabilities of ordinal patterns.
Main Results:
- Unveiled distinct dynamical regimes within the chaotic range.
- Characterized these regimes by unique ordinal pattern hierarchies and probabilities.
- Revealed a correlation between Lyapunov exponent and permutation entropy.
Conclusions:
- Ordinal pattern analysis provides a powerful tool for uncovering hidden dynamics in chaotic systems.
- Dips in the Lyapunov exponent signify transitions between different dynamical regimes.
- This research offers valuable insights for experiments in the semi-classical regime and quantum chaos.
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