  We propose a stationary system that might be regarded as a migration model of
some population abandoning their original place of abode and becoming part of
another population, once they reach the interface boundary. To do so, we show a
model where each population follows a logistic equation in their own
environment while assuming spatial heterogeneities. Moreover, both populations
are coupled through the common boundary, which acts as a permeable membrane on
which their flow moves in and out. The main goal we face in this work will be
to describe the precise interplay between the stationary solutions with respect
to the parameters involved in the problem, in particular the growth rate of the
populations and the coupling parameter involved on the boundary where the
interchange of flux is taking place.
