Inoue Kei
Faculty of Engineering, Sanyo-Onoda City University, 1-1-1 Daigaku-Dori, Sanyo-Onoda 756-0884, Yamaguchi, Japan.
Entropy (Basel). 2021 Nov 14;23(11):1511. doi: 10.3390/e23111511.
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.
李雅普诺夫指数主要用于量化动力系统的混沌程度。然而，从时间序列计算动力系统的李雅普诺夫指数是困难的。熵混沌度是通过信息动力学量化动力系统混沌的一个准则，它对于任何时间序列都可直接计算。然而，对于任何混沌映射，它需要比李雅普诺夫指数更高的值。因此，引入了典型混沌条件下一维混沌映射的改进熵混沌度，以减小李雅普诺夫指数与熵混沌度之间的差异。此外，改进的熵混沌度被扩展到多维混沌映射。最近，作者表明在典型混沌条件下，扩展的熵混沌度与李雅普诺夫指数的总和取相同的值。然而，作者对一些数，特别是映射点的数量假设了无穷大的值。然而，在实际数值计算中，这些数被视为有限的。本研究提出了扩展熵混沌度的改进计算公式，以获得二维混沌映射的适当数值计算结果。
