  We perform a dynamical system analysis of a cosmological model with linear
dependence between the vacuum density and the Hubble parameter, with
constant-rate creation of dark matter. We show that the de Sitter spacetime is
an asymptotically stable critical point, future limit of any expanding
solution. Our analysis also shows that the Minkowski spacetime is an unstable
critical point, which eventually collapses to a singularity. In this way, such
a prescription for the vacuum decay not only predicts the correct future de
Sitter limit, but also forbids the existence of a stable Minkowski universe. We
also study the effect of matter creation on the growth of structures and their
peculiar velocities, showing that it is inside the current errors of redshift
space distortions observations.
