The Dynamics of Non-homogeneous Markov Chains Associated with the b-bistochastic Quadratic Stochastic Operators on 1-dimensional Simplex
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.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
p-Adic Analysis and Mathematical Physics
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- Malaysian Journal of Fundamental and Applied Sciences
- Volume
- 22
- Issue
- 1
- Pages
- 51–60
- Publication date
- 27 February 2026
- Language
- EN