Volterra quadratic stochastic operators of a two-sex population

We introduce the notion of Volterra quadratic stochastic operators of a two-sex population. The fixed points of Volterra quadratic stochastic operators of a two-sex population is studied. Several Lyapunov functions are constructed for these operators. An upper bound for the limit set of trajectories is obtained. It is shown that the set of all Volterra quadratic stochastic operators of a two-sex population is a convex compact set, and the extreme points of this set are found. Volterra quadratic stochastic operators of a two-sex population that have a 2-periodic orbit (trajectory) are constructed.