Gunther Ivan, Pattanayak Arjendu K, Aragoneses Andrés
Department of Physics and Astronomy, Carleton College, 1 N College St, Northfield, Minnesota 55057, USA.
Department of Physics, Eastern Washington University, Cheney, Washington 99004, USA.
Chaos. 2021 Feb;31(2):023104. doi: 10.1063/5.0037999.
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 that is 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.
序数模式是一种时间序列数据分析工具，用作构建排列熵的初步步骤，排列熵本身能够像李雅普诺夫指数等更多理论结构一样对动力学进行混沌或规则的相同表征。然而，序数模式存储的信息严格多于排列熵或李雅普诺夫指数。我们展示了使用杜芬振子的研究结果，表明序数模式反映了动力学对称性的变化，而其他测量方法（甚至排列熵）都无法察觉这种变化。我们发现，在给定参数值下这些对称性变化与相邻参数处稳定性的变化相关，这表明这种分析技术具有一种新的预测能力。
