Global analysis of a model of competition in the chemostat with internal inhibitor

A model of two microbial species in a chemostat competing for single resource the presence an internal inhibitor is considered. The four-dimensional system ordinary differential equations. Using general growth rate functions species, we give complete analysis existence and local stability all steady states. We describe behavior with respect to operating parameters represented by dilution input concentrations substrate. diagram has as its coordinates various regions defined it correspond qualitatively different asymptotic behavior: washout, competitive exclusion one coexistence bistability, multiplicity positive This bifurcation which determines effect parameters, very useful understand from both mathematical biological points view, often constructed literature.