On Quadratic Stochastic Operators Having Three Fixed Points

Algebra, Analysis and Quantum Probability

Saburov, Mansoor^1 ; Yusof, Nur Atikah^1

Department of Computational and Theoretical Sciences, Faculty of Science, International Islamic University Malaysia, P.O. Box, Pahang, Kuantan

25200, Malaysia^1

关键词: Fixed points;    Initial point;    Positive coefficients;    Stochastic matrices;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/697/1/012012/pdf
DOI  :  10.1088/1742-6596/697/1/012012

来源: IOP

【 摘 要 】

We knew that a trajectory of a linear stochastic operator associated with a positive square stochastic matrix starting from any initial point from the simplex converges to a unique fixed point. However, in general, the similar result for a quadratic stochastic operator associated with a positive cubic stochastic matrix does not hold true. In this paper, we provide an example for the quadratic stochastic operator with positive coefficients in which its trajectory may converge to different fixed points depending on initial points.