  We consider a Friedmann model of the universe with bulk viscous matter and
radiation as the cosmic components. We study the asymptotic properties in the
equivalent phase space by considering the three cases for the bulk viscous
coefficient as (i) $\zeta = \zeta_{0}$, a constant (ii) $\zeta = \zeta_{0} +
\zeta_{1}\frac{\dot{a}}{a}$, depending on velocity of the expansion of the
universe and (iii) $\zeta = \zeta_{0} + \zeta_{1}\frac{\dot{a}}{a} +
\zeta_{2}\frac{\ddot{a}}{\dot{a}}$, depending both on velocity and acceleration
of the expansion of the universe. It is found that all the three cases predicts
the late acceleration of the universe. However, a conventional realistic
behaviour of the universe, i.e., a universe having an initial radiation
dominated phase and then followed by decelerated matter dominated phase and
then finally evolving to accelerated epoch, is shown only when $\zeta =
\zeta_{0}$, a constant. For the other two cases, it does not show either a
prior conventional radiation dominated phase or a matter dominated phase of the
universe.
