ON ONE OF THE FAMILY OF EVOLUTION OPERATORS

Abstract

In this paper we study dynamical systems generated by a gonosomal evolution operator of a bisexual population. We find explicitly all (uncountable set) of fixed points of the operator. It is shown that each fixed point has eigenvalues less or equal to 1. Moreover, we show that each trajectory converges to a fixed point, i.e. the operator is reqular. There are uncountable family of invariant sets each of which consisting unique fixed point. Thus there is one-to-one correspondence between such invariant sets and the set of fixed points. Any trajectory started at a point of the invariant set converges to the corresponding fixed point.