The dynamics of non-homogeneous markov chains associated with the b-bistochastic quadratic stochastic operators on 1-dimensional simplex

Azman, Abdurrahman and Wan Rozali, Wan Nur Fairuz Alwani and Mukhamedov, Farrukh (2026) The dynamics of non-homogeneous markov chains associated with the b-bistochastic quadratic stochastic operators on 1-dimensional simplex. Malaysian Journal of Fundamental and Applied Sciences, 22 (1). pp. 51-60. ISSN 2289-5981 E-ISSN 2289-599X

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Abstract

This research investigates the dynamics of a quadratic stochastic operator (QSO), namely the b-bistochastic QSO defined on a 1-dimensional simplex as well as the dynamics of a non-homogeneous Markov chain (NHMC) associated with the said QSO. The QSO was first constructed on a 1-dimensional simplex and a fixed-point analysis was performed onto the constructed QSO. The limiting behavior of the QSO was also studied in order to find its rate of convergence. The QSO was then associated with an NHMC to determine its ergodicity by using an ergodicity coefficient called the Dobrushin ergodicity coefficient. The QSO was found to converge to its attracting fixed point at a constant rate of convergence, and the NHMC associated with the QSO was found to be weakly ergodic

Item Type:	Article (Journal)
Uncontrolled Keywords:	b-order majorization, hyperbolicity, rate of convergence, Dobrushin ergodicity coefficient, weak ergodicity
Subjects:	Q Science > QA Mathematics Q Science > QA Mathematics > QA273 Probabilities
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 Wan Nur Fairuz Alwani Binti Wan Rozali
Date Deposited:	10 Mar 2026 15:25
Last Modified:	10 Mar 2026 15:25
Queue Number:	2026-03-Q2524
URI:	http://irep.iium.edu.my/id/eprint/127867

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