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

Ganikhodjaev, N. N. and Pah, Chin Hee and Rozikov, U. (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

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Abstract

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.

Item Type: Article (Journal)
Additional Information: 5826/91903
Uncontrolled Keywords: China’s five element philosophy; quadratic stochastic operator; fixed point; periodic point; trajectory
Subjects: Q Science > QA Mathematics > QA300 Analysis
Kulliyyahs/Centres/Divisions/Institutes (Can select more than one option. Press CONTROL button): Kulliyyah of Science
Kulliyyah of Science > Department of Computational and Theoretical Sciences
Depositing User: DR. CHIN HEE PAH
Date Deposited: 03 Sep 2021 09:15
Last Modified: 03 Sep 2021 09:15
URI: http://irep.iium.edu.my/id/eprint/91903

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