区分噪声与混沌：使用水平可见度图的客观与主观标准
Distinguishing noise from chaos: objective versus subjective criteria using Horizontal Visibility Graph
摘要：
最近提出的称为水平可见性图（HVG）的方法[Luque { \it et al.}，物理修订版E，80，046103（2009）]，其构成了众所周知的可见性图算法[Lacasa { \it et al.\/}，Proc. Natl. Sci. U.S.A. 105，4972（2008）]，已经被用于研究时间序列中的确定性分量和随机性分量之间的区别[L. Lacasa和R. Toral，Phys. Rev. E.，82，036120（2010）]。具体而言，作者提出，这些过程的节点度分布遵循指数泛函的形式$P(κ)\sim \exp(-λ~κ)$，其中$κ$是节点度和$λ$是一个积极的参数，能够区分确定性（混沌）和随机（不相关和相关）的动态。在这项工作中，我们研究的节点度分布的特性，通过使用HVG构造，对应于$28$混沌映射和$3$不同的随机过程的时间序列。我们深入研究了拉卡萨和托拉尔提出的方法，发现他们的假设是无效的几个案例。我们提出了一种方法，使用HVG与信息论量词。通过对应用HVG获得的节点度分布进行广泛而仔细的分析，我们可以得出这样的结论：Fisher-Shannon信息平面是一个出色的工具，能够以图形方式表示所研究系统的不同性质（确定性或随机性）。
英文摘要：
A recently proposed methodology called the Horizontal Visibility Graph (HVG) [Luque {\it et al.}, Phys. Rev. E., 80, 046103 (2009)] that constitutes a geometrical simplification of the well known Visibility Graph algorithm [Lacasa {\it et al.\/}, Proc. Natl. Sci. U.S.A. 105, 4972 (2008)], has been used to study the distinction between deterministic and stochastic components in time series [L. Lacasa and R. Toral, Phys. Rev. E., 82, 036120 (2010)]. Specifically, the authors propose that the node degree distribution of these processes follows an exponential functional of the form $P(κ)\sim \exp(-λ~κ)$, in which $κ$ is the node degree and $λ$ is a positive parameter able to distinguish between deterministic (chaotic) and stochastic (uncorrelated and correlated) dynamics. In this work, we investigate the characteristics of the node degree distributions constructed by using HVG, for time series corresponding to $28$ chaotic maps and $3$ different stochastic processes. We thoroughly study the methodology proposed by Lacasa and Toral finding several cases for which their hypothesis is not valid. We propose a methodology that uses the HVG together with Information Theory quantifiers. An extensive and careful analysis of the node degree distributions obtained by applying HVG allow us to conclude that the Fisher-Shannon information plane is a remarkable tool able to graphically represent the different nature, deterministic or stochastic, of the systems under study.
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