  We consider quadratic stochastic operators, which are separable as a product
of two linear operators. Depending on properties of these linear operators we
classify the set of the separable quadratic stochastic operators: first class
of constant operators, second class of linear and third class of nonlinear
(separable) quadratic stochastic operators. Since the properties of operators
from the first and second classes are well-known, we mainly study properties of
the operators of the third class. We describe some Lyapunov functions of the
operators and apply them to study $\omega$-limit sets of the trajectories
generated by the operators. Also we compare our results with known results of
the theory of quadratic operators and give some open problems.
