On uniqueness of fixed points of positive quadratic stochastic operators - Saburov, Mansoor (2015)
We know from the theory of Markov chains that any positive square stochastic matrix has a unique fixed point in the simplex and its trajectory starting from any initial point of the simplex converges to that unique fixed point. However, in general, the similar result for a positive cubic stochastic matrix does not hold true. We know that a cubic stochastic matrix is associated with a quadratic stochastic operator defined on the simplex. In this paper, we provide a uniqueness criterion for fixed points of positive quadratic stochastic operators defined on 2D simplex.