Exploring the complex dynamics of a Duffing oscillator with ordinal patterns analysis

TL;DR

This paper investigates the complex dynamics of a Duffing oscillator using ordinal pattern analysis, revealing new dynamical regimes and correlations with chaos indicators that are not detectable by traditional methods.

Contribution

It introduces ordinal pattern analysis to study the Duffing oscillator's dynamics, uncovering regimes and transitions in chaos not seen with conventional statistical tools.

Findings

Different dynamical regimes within chaos identified

Correlation between Lyapunov exponent and permutation entropy established

Dips in Lyapunov exponent linked to dynamical transitions

Abstract

The driven double-well Duffing oscillator is a well-studied system that manifests a wide variety of dynamics, from periodic behavior to chaos, and describing 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 to interpret dips in the Lyapunov exponent as transitions in the dynamics of the system.