  The limit behavior of trajectories of dissipative quadratic stochastic
operators on a finite-dimensional simplex is fully studied. It is shown that
any dissipative quadratic stochastic operator has either unique or infinitely
many fixed points. If dissipative quadratic stochastic operator has a unique
point, it is proven that the operator is regular at this fixed point. If it has
infinitely many fixed points, then it is shown that $\omega-$ limit set of the
trajectory is contained in the set of fixed points.
