Stability of fixed points of discrete dynamic systems of Volterra type

Abstract

In problems of population genetics, we need to study the evolution of biological systems with respect to time. In many cases, the evolution of a system is described by quadratic mappings of a simplex into itself. As is known, every quadratic stochastic operator of Volterra type given on a finite-dimensional simplex defines a certain tournament. This paper introduces the concept of a homogeneous tournament and studies the stability of fixed points of discrete dynamical systems of Volterra operators corresponding to homogeneous tournaments in the simplex S4.