On (s,t)-Volterra Quadratic Stochastic Operators of a Bisexual Population

Abstract

The authors introduce the concept of (s,t)-Volterra stochastic quadratic operator in a bisexual population, where each individual belongs either to the male sex group or female sex group. Under some conditions affecting the coefficients of these operators, several Lyapunov functions have been constructed so that the upper bounds for the set of limiting points of the trajectories could be obtained. This study depicts that the set of (s,t)-Volterra stochastic quadratic operators is a convex compact set and the extreme points of this set are found. Furthermore, (s,t)-Volterra stochastic quadratic operators of the aforementioned population, which have periodic trajectories, are constructed.