Volterra quadratic stochastic operators of a two-sex population

Abstract

We introduce the notion of Volterra quadratic stochastic operators of a two-sex population. The description of the fixed points of Volterra quadratic stochastic operators of a two-sex population is reduced to the description of the fixed points of Volterra-type operators. Several Lyapunov functions are constructed for the Volterra quadratic stochastic operators of a two-sex population. By using these functions, we obtain an upper bound for the ω-limit set of trajectories. 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. © 2011 Springer Science+Business Media, Inc.