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.
In this paper the quadratic stochastic operators (QSO) were considered, these operators describe the population dynamic system. Some quadratic stochastic operators were studied by Lotka and Volterra. Moreover, we discuss the dynamic of some parametric operators from the class of ζ (as) -QSO.The quadratic stochastic operator (QSO) is a mapping of the simplex
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