Hetzer and Shen [3] considered a system
of a two-species Lotka-Volterra competition model with an
inhibitor, investigated its long-term behavior and proposed two
open questions: one is whether the system has a nontrivial
periodic solution; the other is whether one of two positive
equilibria is non-hyperbolic in the case that the system has
exactly two positive equilibria. The goal of this paper is first
to give these questions clear answers, then to present a complete
classification for its dynamics in terms of coefficients. As a
result, all solutions are convergent as $t$ goes to infinity.