On the dynamics of non-Volterra quadratic operators corresponding to permutations

In this talk, we present the results concerning the dynamics of a non-Volterra quadratic stochastic operator defined on a finite-dimensional simplex. We examine the sets of fixed points and periodic points for this operator. Moreover, we show that the set of limit points for any trajectory of such a non-Volterra quadratic stochastic operator consists of either a single point or a finite set of points.