  We investigate the generalized contact process with two absorbing states in
one space dimension by means of large-scale Monte-Carlo simulations. Treating
the creation rate of active sites between inactive domains as an independent
parameter leads to a rich phase diagram. In addition to the conventional active
and inactive phases we find a parameter region where the simple contact process
is inactive, but an infinitesimal creation rate at the boundary between
inactive domains is sufficient to take the system into the active phase. Thus,
the generalized contact process has two different phase transition lines. The
point separating them shares some characteristics with a multicritical point.
We also study in detail the critical behaviors of these transitions and their
universality.
