In this article, we present a mathematical six-dimensional dynamical
system involving a three-tiered microbial food web without maintenance.
We give a qualitative analysis of the model, and an analysis of the local
stability of equilibrium points.
Under general assumptions of monotonicity, we prove the uniqueness and the
local stability of the positive equilibrium point corresponding to the
persistence of the three bacteria. Possibilities of periodic orbits are
not excluded and asymptotic coexistence is satisfied