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

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.

12 pages, 6 figures

References in corpus (7)

• Predictability: a way to characterize Complexity
• Quantum interference between two single photons emitted by independently trapped atoms
• Characterizing Time Series via Complexity-Entropy Curves
• Unveiling temporal correlations characteristic to phase transition in the intensity of a fibre laser radiation
• Persistence and Stochastic Periodicity in the Intensity Dynamics of a Fiber Laser During the Transition to Optical Turbulence
• Observing quantum chaos with noisy measurements and highly mixed states
• Dynamical complexity in the quantum to classical transition