Trostel Max L, Misplon Moses Z R, Aragoneses Andrés, Pattanayak Arjendu K
Department of Physics and Astronomy, Carleton College, Northfield, MN 55057, USA.
Entropy (Basel). 2018 Jan 10;20(1):40. doi: 10.3390/e20010040.
The driven double-well Duffing oscillator is a well-studied system that manifests a wide variety of dynamics, from periodic behavior to chaos, and describes 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 us to interpret dips in the Lyapunov exponent as transitions in the dynamics of the system.
受迫双阱杜芬振子是一个经过充分研究的系统，它展现出从周期性行为到混沌等各种各样的动力学特性，并描述了一系列不同的物理系统。它已被证明与理解从经典到量子转变中的混沌现象相关。在此，我们使用序数模式分析技术来探索其在经典和半经典区域的动力学复杂性。这对于半经典区域的潜在实验尤为重要。我们揭示了混沌范围内不同的动力学区域，而这些区域用更传统的统计工具是无法检测到的。这些区域的特征在于序数模式的不同层次结构和概率。我们发现了李雅普诺夫指数与排列熵之间的相关性，这使我们将李雅普诺夫指数中的下降解释为系统动力学的转变。
