Hirata Yoshito, Aihara Kazuyuki
Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Sep;82(3 Pt 2):036209. doi: 10.1103/PhysRevE.82.036209. Epub 2010 Sep 23.
Although the definition of deterministic chaos in the sense of Devaney is often employed for investigating dynamical systems, it has been rarely used for identifying deterministic chaos from time series. In this paper, we develop a set of methods that infers whether a given time series is consistent with deterministic chaos in the sense of Devaney or not. We define weaker notions of the three properties of Devaney's chaos which can be checked using a given time series of a finite length. We apply these methods for artificial and real data.
虽然在研究动力系统时，常采用迪瓦尼意义下的确定性混沌定义，但它很少用于从时间序列中识别确定性混沌。在本文中，我们开发了一套方法，用于推断给定的时间序列是否与迪瓦尼意义下的确定性混沌一致。我们定义了迪瓦尼混沌三个性质的较弱概念，这些概念可以通过给定的有限长度时间序列进行检验。我们将这些方法应用于人工数据和真实数据。
