An Improved Calculation Formula of the Extended Entropic Chaos Degree and Its Application to Two-Dimensional Chaotic Maps.
An Improved Calculation Formula of the Extended Entropic Chaos Degree and Its Application to Two-Dimensional Chaotic Maps.
复制标题
DOI：
10.3390/e23111511
复制
发表时间：
2021-11-14
期刊：
影响因子：
--
通讯作者：
Inoue K
中科院分区：
文献类型：
--
作者：
Inoue K
李雅普诺夫指数主要用于量化动力系统的混沌度。然而，从时间序列计算动力系统的李亚普诺夫指数是很困难的。熵混沌度是通过信息动力学量化动力系统混沌的标准，对于任何时间序列都可以直接计算。然而，对于任何混沌映射，它都需要比 Lyapunov 指数更高的值。因此，引入典型混沌条件下一维混沌映射的改进熵混沌度来减小Lyapunov指数与熵混沌度之间的差异。此外，改进的熵混沌度被推广到多维混沌映射。最近，作者证明了在典型混沌条件下，扩展熵混沌度与Lyapunov指数总和的值相同。然而，作者假设某些数字的值为无穷大，尤其是映射点的数量。然而，在实际的数值计算中，这些数字被视为有限的。本研究提出了一种改进的扩展熵混沌度计算公式，以获得二维混沌映射合适的数值计算结果。
The Lyapunov exponent is primarily used to quantify the chaos of a dynamical system. However, it is difficult to compute the Lyapunov exponent of dynamical systems from a time series. The entropic chaos degree is a criterion for quantifying chaos in dynamical systems through information dynamics, which is directly computable for any time series. However, it requires higher values than the Lyapunov exponent for any chaotic map. Therefore, the improved entropic chaos degree for a one-dimensional chaotic map under typical chaotic conditions was introduced to reduce the difference between the Lyapunov exponent and the entropic chaos degree. Moreover, the improved entropic chaos degree was extended for a multidimensional chaotic map. Recently, the author has shown that the extended entropic chaos degree takes the same value as the total sum of the Lyapunov exponents under typical chaotic conditions. However, the author has assumed a value of infinity for some numbers, especially the number of mapping points. Nevertheless, in actual numerical computations, these numbers are treated as finite. This study proposes an improved calculation formula of the extended entropic chaos degree to obtain appropriate numerical computation results for two-dimensional chaotic maps.
登录
查看更多内容
影响因子：
2.4
作者：
IKEDA, K
通讯作者：
IKEDA, 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.