On a Superposition of Volterra and Permuted Volterra Quadratic Stochastic Operators

In the present paper, we study dynamical systems generated by stochastic operators which are superpositions of extremal Volterra and non-Volterra quadratic stochastic operators defined on the two-dimensional simplex. It is described the set of all periodic and the set of all fixed points of such operators. Further for such operator we showed that for an initial point their trajectory either converges to a periodic trajectory or diverges.