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Characterizing Complex Dynamics in the Classical and Semi-Classical Duffing Oscillator Using Ordinal Patterns Analysis

Department of Physics and Astronomy, Carleton College, Northfield, MN 55057, USA
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Entropy 2018, 20(1), 40; https://doi.org/10.3390/e20010040
Received: 20 December 2017 / Revised: 3 January 2018 / Accepted: 5 January 2018 / Published: 10 January 2018
(This article belongs to the Special Issue Permutation Entropy & Its Interdisciplinary Applications)
The driven double-well Duffing oscillator is a well-studied system that manifests a wide variety of dynamics, from periodic behavior to chaos, and describes a diverse array of physical systems. It has been shown to be relevant in understanding chaos in the classical to quantum transition. Here we explore the complexity of its dynamics in the classical and semi-classical regimes, using the technique of ordinal pattern analysis. This is of particular relevance to potential experiments in the semi-classical regime. We unveil different dynamical regimes within the chaotic range, which cannot be detected with more traditional statistical tools. These regimes are characterized by different hierarchies and probabilities of the ordinal patterns. Correlation between the Lyapunov exponent and the permutation entropy is revealed that leads us to interpret dips in the Lyapunov exponent as transitions in the dynamics of the system. View Full-Text
Keywords: complex dynamics; Duffing oscillator; permutation entropy; chaos; semiclassical transition complex dynamics; Duffing oscillator; permutation entropy; chaos; semiclassical transition
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MDPI and ACS Style

Trostel, M.L.; Misplon, M.Z.R.; Aragoneses, A.; Pattanayak, A.K. Characterizing Complex Dynamics in the Classical and Semi-Classical Duffing Oscillator Using Ordinal Patterns Analysis. Entropy 2018, 20, 40. https://doi.org/10.3390/e20010040

AMA Style

Trostel ML, Misplon MZR, Aragoneses A, Pattanayak AK. Characterizing Complex Dynamics in the Classical and Semi-Classical Duffing Oscillator Using Ordinal Patterns Analysis. Entropy. 2018; 20(1):40. https://doi.org/10.3390/e20010040

Chicago/Turabian Style

Trostel, Max L.; Misplon, Moses Z.R.; Aragoneses, Andrés; Pattanayak, Arjendu K. 2018. "Characterizing Complex Dynamics in the Classical and Semi-Classical Duffing Oscillator Using Ordinal Patterns Analysis" Entropy 20, no. 1: 40. https://doi.org/10.3390/e20010040

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