On quadratic stochastic operators having three fixed points

• Main Authors: Saburov, Mansoor, Yusof, Nur Atikah
• Format: Article
• Language: English; English
• Published: Institute of Physics Publishing (UK) 2016
• Subjects: QA Mathematics
• Online Access: http://irep.iium.edu.my/51149/3/51149.pdf; http://irep.iium.edu.my/51149/4/51149_On_Quadratic_Stochastic_Operators_Having_Three_Fixed_Points_SCOPUS.pdf; http://irep.iium.edu.my/51149/; http://iopscience.iop.org/article/10.1088/1742-6596/697/1/012012/pdf

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.