An Improved Calculation Formula of the Extended Entropic Chaos Degree and Its Application to Two-Dimensional Chaotic Maps

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, wh...

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Autor principal:	Kei Inoue
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	chaos Lyapunov exponent extended entropic chaos degree Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/a83742857c294f66a7044e080b6deafe
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id	oai:doaj.org-article:a83742857c294f66a7044e080b6deafe
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spelling	oai:doaj.org-article:a83742857c294f66a7044e080b6deafe2021-11-25T17:30:23ZAn Improved Calculation Formula of the Extended Entropic Chaos Degree and Its Application to Two-Dimensional Chaotic Maps10.3390/e231115111099-4300https://doaj.org/article/a83742857c294f66a7044e080b6deafe2021-11-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1511https://doaj.org/toc/1099-4300The 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.Kei InoueMDPI AGarticlechaosLyapunov exponentextended entropic chaos degreeScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1511, p 1511 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	chaos Lyapunov exponent extended entropic chaos degree Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	chaos Lyapunov exponent extended entropic chaos degree Science Q Astrophysics QB460-466 Physics QC1-999 Kei Inoue An Improved Calculation Formula of the Extended Entropic Chaos Degree and Its Application to Two-Dimensional Chaotic Maps
description	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.
format	article
author	Kei Inoue
author_facet	Kei Inoue
author_sort	Kei Inoue
title	An Improved Calculation Formula of the Extended Entropic Chaos Degree and Its Application to Two-Dimensional Chaotic Maps
title_short	An Improved Calculation Formula of the Extended Entropic Chaos Degree and Its Application to Two-Dimensional Chaotic Maps
title_full	An Improved Calculation Formula of the Extended Entropic Chaos Degree and Its Application to Two-Dimensional Chaotic Maps
title_fullStr	An Improved Calculation Formula of the Extended Entropic Chaos Degree and Its Application to Two-Dimensional Chaotic Maps
title_full_unstemmed	An Improved Calculation Formula of the Extended Entropic Chaos Degree and Its Application to Two-Dimensional Chaotic Maps
title_sort	improved calculation formula of the extended entropic chaos degree and its application to two-dimensional chaotic maps
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/a83742857c294f66a7044e080b6deafe
work_keys_str_mv	AT keiinoue animprovedcalculationformulaoftheextendedentropicchaosdegreeanditsapplicationtotwodimensionalchaoticmaps AT keiinoue improvedcalculationformulaoftheextendedentropicchaosdegreeanditsapplicationtotwodimensionalchaoticmaps
_version_	1718412304274423808

An Improved Calculation Formula of the Extended Entropic Chaos Degree and Its Application to Two-Dimensional Chaotic Maps

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