  We revisit the dynamical system based approach of spherically symmetric
vacuum braneworlds, pointing out and studying the existence of a transcritical
bifurcation as the dark pressure parameter changes its sign, we analyze some
consequences of not discard the brane cosmological constant. For instance, it
is noteworthy that the existence of an isothermal state equation between the
dark fluid parameters cannot be obtained via the requirement of a
quasi-homologous symmetry of the vacuum.
