  This paper studies a two-dimensional chemotactic model for two species in
which one of them produces a chemo-repellent for the other. It is shown
asymptotically and numerically how the chemical inhibits the invasion of a
moving front for the second species and how stable steady states, which depend
on the chemical concentration, can be reached. The results qualitatively
explain experimental observations by Swain and Ray (Microbiol. Res. 164(2),
2009), where colonies of bacteria produce metabolite agents which prevent the
invasion of fungi.
