Abstract

In this work, we present a comprehensive assessment of the Fisher information measure and statistical complexity measures based on Euclidean distance, Wootters distance and Jensen–Shannon divergence, regarding their abilities to (planar-) distinguish between/among (1) chaos and periodicity; (2) different degrees of periodicities; (3) different chaotic regimes; and (4) chaos and noise, and characterize delay dynamics. The Bandt–Pompe approach is used to build up the probability space to generate the entropy-complexity/information plane. The effect of embedding parameters on the evaluation is also considered. Within this framework, complexity measures based on the Wootters distance and Jensen–Shannon divergence are superior to the Fisher information measure in capturing subtle details of chaotic dynamics. The Fisher information measure shows advantages in robustness to additive noises and in planar-behavior representation of chaos and noise. Moreover, all measures are able to properly characterize the intrinsic delay dynamics of chaotic and stochastic systems. Nevertheless, the complexity measure based on the Euclidean distance is not valid by definition, thus, not applicable at any cases.

中文翻译：

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混沌和噪声平面表征中的复杂性和信息措施

摘要

在这项工作中，我们对基于Fisher距离，Wooters距离和Jensen-Shannon散度的Fisher信息量度和统计复杂性量度进行了全面评估，评估了它们在（平面）上区分（/）（1）混沌和周期性的能力；（2）不同程度的周期性；（3）不同的混乱状态；（4）混沌和噪声，表征延迟动态。Bandt–Pompe方法用于建立概率空间以生成熵复杂度/信息平面。还考虑了参数嵌入对评估的影响。在此框架内，基于伍特斯距离和詹森-香农散度的复杂性度量在捕获混沌动力学的细微细节方面优于费舍尔信息度量。Fisher信息量度显示出对加性噪声的鲁棒性以及对混沌和噪声的平面行为表示的优势。此外，所有措施都能够恰当地表征混沌和随机系统的固有延迟动力学。然而，基于欧几里德距离的复杂性度量在定义上是无效的，因此，在任何情况下都不适用。