  In this note we present a study of the solutions associated to a particular
spatial extension of the Rosenzweig-MacArthur model for predator and prey. The
analysis presented here shows that positive steady state solutions emerge via a
transcritical bifurcation mechanism, in accordance with the insight obtained
from previous numerical and analytical results. In the model under discussion,
prey is assumed to move avoiding crowds via a density-dependent diffusion and
also incorporates the existence of a refuge zone, where predators cannot
consume prey. Saturation in prey consumption is also included through a Holling
type II functional response.
