AI 中文总结
本研究提出一种结合归一化排列熵与归一化排列互信息的二维量化平面，用于分析时间序列，可表征变量不确定性与共享信息，揭示变量间方向性，并通过规则、混沌、随机动力学验证其有效性。
AI 中文摘要
本研究提出一种新的二维量化平面，结合了归一化排列熵与归一化排列互信息，二者均源自香农信息论，并通过Bandt和Pompe方法的嵌入维度进行一致归一化。平面上的每个点可同时表征变量的固有不确定性及其与另一变量共享的信息量。我们进一步表明，第三个量（等价于一个变量给定另一变量的条件熵）引入了信息独立性的概念，当联合考虑变量对的两个投影时，可揭示它们之间的方向性。我们分析了规则、混沌和随机动力学，以说明该信息平面的相关性，并展示这些动力学如何随耦合因子变化。
英文摘要
This work presents a new two-dimensional quantifier plane that combines normalized permutation entropy and normalized permutation mutual information, both derived from Shannon's information theory and normalized consistently through the embedding dimension of the Bandt and Pompe method. Each point on the plane simultaneously characterizes the intrinsic uncertainty of a variable and the amount of information it shares with another. We further show that a third quantity, equivalent to the conditional entropy of one variable given the other, introduces a notion of informational independence and, when both projections of a variable pair are considered jointly, reveals directionality between them. We analyze regular, chaotic, and stochastic dynamics to illustrate the relevance of the informational plane and show how these regimes evolve as a function of a coupling factor.
Comments11 pages, 4 figures
