Duffing振子复杂动力学的有序模式分析
Exploring the complex dynamics of a Duffing oscillator with ordinal patterns analysis
摘要：
受驱动双阱Duffing振子是一个被广泛研究的系统，它表现出从周期行为到混沌的各种动力学行为，并描述了各种各样的物理系统。它已被证明是相关的理解在经典到量子过渡的混沌。在这里，我们探讨其动态的复杂性，在经典和半经典的制度，使用有序模式分析的技术。这是特别相关的潜在实验在半经典制度。我们揭示了不同的动力学制度的混沌范围内，这不能用更传统的统计工具检测。这些政权的特点是不同的层次和概率的顺序模式。揭示了李雅普诺夫指数和置换熵之间的相关性，从而解释了李雅普诺夫指数的下降作为系统动力学的转变。
英文摘要：
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.
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