  The present paper focuses on the dynamical systems of the quadratic
bistochastic operators (QBO) on the standard simplex. In the paper, we show the
character of connection of the dynamical systems of a bistochastic operator
with the dynamical systems of the extreme bistochastic operators. In addition,
we prove that almost all quadratic bistochastic operators are strictly regular
and give a description of the strictly regular quadratic bistochastic operators
in the convex polytope QBO. Furthermore, the density of the set of strictly
regular QBO in the set of QBO is proved and nontrivial examples of strictly
regular bistochastic operators are given.
