  We revisit the global dynamics of unified dark matter cosmological models and
analyze it in a new dynamical system setting. In particular, by defining a
suitable set of variables we obtain a bounded variable space, a feature that
allows a better control of the critical elements of the system. First, we give
a comprehensive cosmological interpretation of the critical points. Then, we
turn our focus on particular representative trajectories with physically
motivated initial conditions studied in the first paper of the series, and we
discuss how the scale factor relates to the equation of state parameter. We
review and complement these results in the light of the new variable approach
by discussing the issue whether the system is chaotic or not.
