  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.
