An extension of the entropic chaos degree and its positive effect
An extension of the entropic chaos degree and its positive effect
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DOI：
10.1007/s13160-020-00453-9
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发表时间：
2021-01-03
影响因子：
0.9
通讯作者：
Umeno, Ken
中科院分区：
文献类型：
--
作者：
Inoue, Kei;Mao, Tomoyuki;Umeno, Ken
李雅普诺夫指数通过刻画动力系统初始点的指数敏感度，来量化动力系统的混沌。然而，对于没有动力学方程的动力系统，我们不能直接计算其Lyapunov指数，尽管确实有一些估计方法。信息动力学引入了熵混沌程度来衡量动力系统的混沌强度。对于实际的时间序列，可以用熵混沌度来计算混沌的强度。它可能看起来像是一种有限空间的Kolmogorov-Sinai熵，它表示了熵混沌程度与Lyapunov指数之间的关系。在本文中，我们尝试在d维欧氏空间上推广熵混沌度的定义，以提高测量动力系统混沌强度的能力，并证明扩展的熵混沌度与Lyapunov指数之间的几个关系。
The Lyapunov exponent is used to quantify the chaos of a dynamical system, by characterizing the exponential sensitivity of an initial point on the dynamical system. However, we cannot directly compute the Lyapunov exponent for a dynamical system without its dynamical equation, although some estimation methods do exist. Information dynamics introduces the entropic chaos degree to measure the strength of chaos of the dynamical system. The entropic chaos degree can be used to compute the strength of chaos with a practical time series. It may seem like a kind of finite space Kolmogorov-Sinai entropy, which then indicates the relation between the entropic chaos degree and the Lyapunov exponent. In this paper, we attempt to extend the definition of the entropic chaos degree on a d-dimensional Euclidean space to improve the ability to measure the stength of chaos of the dynamical system and show several relations between the extended entropic chaos degree and the Lyapunov exponent.