Classification of ξ^(s)-Quadratic Stochastic Operators on 2D simplex

A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some QSO has been studied by Lotka and Volterra. The general problem in the nonlinear operator theory is to study the behavior of operators. This problem was not fully finished even for the quadratic stochastic operators. To study this problem it was investigated several classes of such QSO. In this paper we study ξ^(s)-QSO class of operators. We study such kind of operators on 2D simplex. We first classify these ξ^(s)-QSO into 20 classes. Further, we investigate the dynamics of one class of such operators.