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Characterizing Complex Dynamics in the Classical and Semi-Classical Duffing Oscillator Using Ordinal Patterns Analysis
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 ex...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2018
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512236/ https://www.ncbi.nlm.nih.gov/pubmed/33265129 http://dx.doi.org/10.3390/e20010040 |
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author | Trostel, Max L. Misplon, Moses Z. R. Aragoneses, Andrés Pattanayak, Arjendu K. |
author_facet | Trostel, Max L. Misplon, Moses Z. R. Aragoneses, Andrés Pattanayak, Arjendu K. |
author_sort | Trostel, Max L. |
collection | PubMed |
description | 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. |
format | Online Article Text |
id | pubmed-7512236 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2018 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-75122362020-11-09 Characterizing Complex Dynamics in the Classical and Semi-Classical Duffing Oscillator Using Ordinal Patterns Analysis Trostel, Max L. Misplon, Moses Z. R. Aragoneses, Andrés Pattanayak, Arjendu K. Entropy (Basel) Article 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. MDPI 2018-01-10 /pmc/articles/PMC7512236/ /pubmed/33265129 http://dx.doi.org/10.3390/e20010040 Text en © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Trostel, Max L. Misplon, Moses Z. R. Aragoneses, Andrés Pattanayak, Arjendu K. Characterizing Complex Dynamics in the Classical and Semi-Classical Duffing Oscillator Using Ordinal Patterns Analysis |
title | Characterizing Complex Dynamics in the Classical and Semi-Classical Duffing Oscillator Using Ordinal Patterns Analysis |
title_full | Characterizing Complex Dynamics in the Classical and Semi-Classical Duffing Oscillator Using Ordinal Patterns Analysis |
title_fullStr | Characterizing Complex Dynamics in the Classical and Semi-Classical Duffing Oscillator Using Ordinal Patterns Analysis |
title_full_unstemmed | Characterizing Complex Dynamics in the Classical and Semi-Classical Duffing Oscillator Using Ordinal Patterns Analysis |
title_short | Characterizing Complex Dynamics in the Classical and Semi-Classical Duffing Oscillator Using Ordinal Patterns Analysis |
title_sort | characterizing complex dynamics in the classical and semi-classical duffing oscillator using ordinal patterns analysis |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7512236/ https://www.ncbi.nlm.nih.gov/pubmed/33265129 http://dx.doi.org/10.3390/e20010040 |
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