Global and local behavior of a class of ξ(s)-QSO

A quadratic stochastic operator (QSO) describes the time evolution of different species in biology. The main problem with regard to a nonlinear operator is to study its behavior. This has not been studied in depth; even QSOs, which are the simplest nonlinear operators, have not been studied thoroughly. This paper investigates the global behavior of an operator taken from ξ(s)-QSO when the parameter a = 1/2 . Moreover, we study the local behavior of this operator at each value of a, where 0 a 1.