Analysis of Chaotic Dynamics by the Extended Entropic Chaos Degree
Analysis of Chaotic Dynamics by the Extended Entropic Chaos Degree
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DOI：
10.3390/e24060827
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发表时间：
2022-06-14
期刊：
影响因子：
2.7
通讯作者：
Inoue K
中科院分区：
文献类型：
--
作者：
Inoue K
李亚普诺夫指数是最著名的量化动力系统混沌的度量。然而，在没有动力系统信息的情况下对任何时间序列进行计算都具有挑战性，因为需要生成动力系统的映射的雅可比矩阵。熵混沌度将动力系统的混沌程度衡量为信息动力学框架中的信息量，即使动力系统未知，也可以直接计算任何时间序列。最近的一项研究引入了扩展熵混沌度，其在典型混沌条件下达到了与李亚普诺夫指数总和相同的值。此外，最近提出了一种改进的扩展熵混沌度计算公式，以获得多维混沌映射的适当数值计算结果。研究表明，可以估计混沌映射的所有李亚普诺夫指数来计算扩展熵混沌度，并提出了扩展熵混沌度的计算算法；此外，该计算算法还应用于一维和二维混沌映射。结果表明，对于一维和二维混沌动力学，扩展熵混沌度可能是 Lyapunov 指数的可行替代方案。
The Lyapunov exponent is the most-well-known measure for quantifying chaos in a dynamical system. However, its computation for any time series without information regarding a dynamical system is challenging because the Jacobian matrix of the map generating the dynamical system is required. The entropic chaos degree measures the chaos of a dynamical system as an information quantity in the framework of Information Dynamics and can be directly computed for any time series even if the dynamical system is unknown. A recent study introduced the extended entropic chaos degree, which attained the same value as the total sum of the Lyapunov exponents under typical chaotic conditions. Moreover, an improved calculation formula for the extended entropic chaos degree was recently proposed to obtain appropriate numerical computation results for multidimensional chaotic maps. This study shows that all Lyapunov exponents of a chaotic map can be estimated to calculate the extended entropic chaos degree and proposes a computational algorithm for the extended entropic chaos degree; furthermore, this computational algorithm was applied to one and two-dimensional chaotic maps. The results indicate that the extended entropic chaos degree may be a viable alternative to the Lyapunov exponent for both one and two-dimensional chaotic dynamics.
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DOI：
10.3390/e23111511
发表时间：
2021-11-14
期刊：
Entropy (Basel, Switzerland)
影响因子：
--
作者：
Inoue K
通讯作者：
Inoue K
影响因子：
7.8
作者：
Inoue, K;Ohya, M;Sato, K
通讯作者：
Sato, K
影响因子：
1.3
作者：
Inoue, K;Ohya, M;Volovich, IV
通讯作者：
Volovich, IV
DOI：
10.1007/s13160-020-00453-9
发表时间：
2021-01-03
影响因子：
0.9
作者：
Inoue, Kei;Mao, Tomoyuki;Umeno, Ken
通讯作者：
Umeno, Ken
影响因子：
0.8
作者：
Inoue, Kei;Ohya, Masanori;Volovich, Igor V.
通讯作者：
Volovich, Igor V.