Ordinal Patterns in the Duffing Oscillator: Analyzing Powers of Characterization

TL;DR

This paper demonstrates that ordinal patterns in the Duffing oscillator reveal hidden dynamical symmetries and stability changes, offering a more detailed analysis than traditional measures like Permutation Entropy.

Contribution

It introduces the use of ordinal patterns to detect subtle symmetry changes and stability shifts in the Duffing oscillator, surpassing existing analysis methods.

Findings

Ordinal patterns detect symmetry changes invisible to Permutation Entropy.

Changes in symmetry correlate with stability shifts at neighboring parameters.

Ordinal patterns provide potential predictive insights into dynamical stability.

Abstract

Ordinal Patterns are a time-series data analysis tool used as a preliminary step to construct the Permutation Entropy which itself allows the same characterization of dynamics as chaotic or regular as more theoretical constructs such as the Lyapunov exponent. However ordinal patterns store strictly more information than Permutation Entropy or Lyapunov exponents. We present results working with the Duffing oscillator showing that ordinal patterns reflect changes in dynamical symmetry invisible to other measures, even Permutation Entropy. We find that these changes in symmetry at given parameter values are correlated with a change in stability at neighboring parameters which suggests a novel predictive capability for this analysis technique.