利用Fisher-Shannon复杂性计划中排序模式的影响
Exploiting the impact of ordering patterns in the Fisher-Shannon complexity plan
摘要：
Fisher-Shannon复杂性平面是在二维平面中表示复杂动力学的强大工具。它根据系统的熵和Fisher信息测度（Fisher Information Measure，FSI）来确定系统的位置。最近的研究表明，通过使用有序模式来计算排列熵和排列熵，这个平面揭示了系统复杂和混沌动力学背后的结构的内部细节。为了计算模式，模式的顺序非常重要。我们详细分析了排序协议的影响，用于计算使用有序模式的排序。我们展示了一个合适的选择，这可以节省计算资源的重要性，但也揭示了其他排序协议无法访问的动态细节。我们的研究结果与前人的研究结果一致，并发现共同的特征指纹的不同的混沌映射研究。我们的分析还揭示了所研究的混沌映射的分形行为。我们提取了一些基本的对称性，使我们能够模拟的复杂性平面上的混沌政权的控制参数范围很广的行为。
英文摘要：
The Fisher-Shannon complexity plane is a powerful tool that represents complex dynamics in a two-dimensional plane. It locates a dynamical system based upon its entropy and its Fisher Information Measure (FIM). It has been recently shown that, by using ordinal patterns to compute permutation entropy and FIM, this plane unveils inner details of the structure underlying the complex and chaotic dynamics of a system. In order to compute FIM, the order of the patterns is very relevant. We analyze in detail the impact of the sorting protocol used to calculate FIM using ordinal patterns. We show the importance of a suitable choice, which can lead to saving computational resources, but also to unveil details of the dynamics not accessible to other sorting protocols. Our results agree with previous research, and common characteristic fingerprints are found for the different chaotic maps studied. Our analysis also reveals the fractal behavior of the chaotic maps studied. We extract some underlying symmetries that allow us to simulate the behavior on the complexity plane for a wide range of the control parameters in the chaotic regimes.
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