How can inter-specific interferences explain coexistence or confirm the competitive exclusion principle in a chemostat?

In this paper, I consider two species feeding on limiting substrate in a chemostat taking into account some possible effects of each species on the other one. System of differential equations is proposed as model of these effects with general inter-specific density-dependent growth rates. Three cases were considered. The first one for a mutual inhibitory relationship where it is proved that at most one species can survive which confirms the competitive exclusion principle. Initial concentrations of species have great importance in determination of which species is the winner. The second one for a food web relationship where it is proved that under general assumptions on the dilution rate, both species persist for any initial conditions. Finally, a third case dealing with an obligate mutualistic relationship was discussed. It is proved that initial condition has a great importance in determination of persistence or extinction of both species.