The dynamics of (π, α)-cubic stochastic operators

Abstract

In the present paper, we consider non-Volterra cubic stochastic operators defined on a finite-dimensional simplex depending on a permutation π and a parameter α. We showed that for any permutation π, except the identity permutation, the set of limit points of the trajectories corresponding to the operators converges to a periodic trajectory. The trajectories of the operator corresponding to the identity permutation converge to a fixed point.