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Dynamics of quadratic stochastic operators generated by China's five element philosophy

Motivated by the China’s five element philosophy (CFEP), we construct a permuted Volterra quadratic stochastic operator acting on the four-dimensional simplex. This operator (depending on 10 parameters) is considered as an evolution operator for CFEP. We study the discrete-time dynamical system gene...

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Main Authors: Ganikhodjaev, Nasir, Pah, Chin Hee, Rozikov, Utkir Abdulloevich
格式: Article
語言:English
English
出版: Taylor & Francis 2021
主題:
QA300 Analysis
在線閱讀:http://irep.iium.edu.my/91903/7/91903_Dynamics%20of%20quadratic%20stochastic%20operators.pdf
http://irep.iium.edu.my/91903/13/91903_Scopus%20-%20Dynamics%20of%20quadratic%20stochastic%20operators%20generated%20by%20China%27s%20five%20element%20philosophy.pdf
http://irep.iium.edu.my/91903/
https://www.tandfonline.com/doi/full/10.1080/10236198.2021.1968385
http://doi.org/10.1080/10236198.2021.1968385
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spelling my.iium.irep.919032022-01-11T05:37:40Z http://irep.iium.edu.my/91903/ Dynamics of quadratic stochastic operators generated by China's five element philosophy Ganikhodjaev, Nasir Pah, Chin Hee Rozikov, Utkir Abdulloevich QA300 Analysis Motivated by the China’s five element philosophy (CFEP), we construct a permuted Volterra quadratic stochastic operator acting on the four-dimensional simplex. This operator (depending on 10 parameters) is considered as an evolution operator for CFEP. We study the discrete-time dynamical system generated by this operator. Mainly our results related to a symmetric operator (depending on one parameter). We show that this operator has a unique fixed point, which is repeller. Moreover, in the case of non-zero parameter, it has two 5-periodic orbits. We divide the simplex to four subsets: the first set consists a single point (the fixed point); the second (resp. third) set is the set of initial point trajectories of which converge to the first (resp. second) 5-periodic orbit; the fourth subset is the set of initial point trajectories of which do not converge and their sets of limit points are infinite and lie on the boundary of the simplex. We give interpretations of our results to CFEP. Taylor & Francis 2021-09-01 Article PeerReviewed application/pdf en http://irep.iium.edu.my/91903/7/91903_Dynamics%20of%20quadratic%20stochastic%20operators.pdf application/pdf en http://irep.iium.edu.my/91903/13/91903_Scopus%20-%20Dynamics%20of%20quadratic%20stochastic%20operators%20generated%20by%20China%27s%20five%20element%20philosophy.pdf Ganikhodjaev, Nasir and Pah, Chin Hee and Rozikov, Utkir Abdulloevich (2021) Dynamics of quadratic stochastic operators generated by China's five element philosophy. Journal of Difference Equations and Applications. pp. 1-20. ISSN 1023-6198 E-ISSN 1563-5120 https://www.tandfonline.com/doi/full/10.1080/10236198.2021.1968385 http://doi.org/10.1080/10236198.2021.1968385
institution Universiti Islam Antarabangsa Malaysia
building IIUM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider International Islamic University Malaysia
content_source IIUM Repository (IREP)
url_provider http://irep.iium.edu.my/
language English
English
topic QA300 Analysis
spellingShingle QA300 Analysis
Ganikhodjaev, Nasir
Pah, Chin Hee
Rozikov, Utkir Abdulloevich
Dynamics of quadratic stochastic operators generated by China's five element philosophy
description Motivated by the China’s five element philosophy (CFEP), we construct a permuted Volterra quadratic stochastic operator acting on the four-dimensional simplex. This operator (depending on 10 parameters) is considered as an evolution operator for CFEP. We study the discrete-time dynamical system generated by this operator. Mainly our results related to a symmetric operator (depending on one parameter). We show that this operator has a unique fixed point, which is repeller. Moreover, in the case of non-zero parameter, it has two 5-periodic orbits. We divide the simplex to four subsets: the first set consists a single point (the fixed point); the second (resp. third) set is the set of initial point trajectories of which converge to the first (resp. second) 5-periodic orbit; the fourth subset is the set of initial point trajectories of which do not converge and their sets of limit points are infinite and lie on the boundary of the simplex. We give interpretations of our results to CFEP.
format Article
author Ganikhodjaev, Nasir
Pah, Chin Hee
Rozikov, Utkir Abdulloevich
author_facet Ganikhodjaev, Nasir
Pah, Chin Hee
Rozikov, Utkir Abdulloevich
author_sort Ganikhodjaev, Nasir
title Dynamics of quadratic stochastic operators generated by China's five element philosophy
title_short Dynamics of quadratic stochastic operators generated by China's five element philosophy
title_full Dynamics of quadratic stochastic operators generated by China's five element philosophy
title_fullStr Dynamics of quadratic stochastic operators generated by China's five element philosophy
title_full_unstemmed Dynamics of quadratic stochastic operators generated by China's five element philosophy
title_sort dynamics of quadratic stochastic operators generated by china's five element philosophy
publisher Taylor & Francis
publishDate 2021
url http://irep.iium.edu.my/91903/7/91903_Dynamics%20of%20quadratic%20stochastic%20operators.pdf
http://irep.iium.edu.my/91903/13/91903_Scopus%20-%20Dynamics%20of%20quadratic%20stochastic%20operators%20generated%20by%20China%27s%20five%20element%20philosophy.pdf
http://irep.iium.edu.my/91903/
https://www.tandfonline.com/doi/full/10.1080/10236198.2021.1968385
http://doi.org/10.1080/10236198.2021.1968385
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score 13.251813

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