Dynamics of a chemostat in which two organisms compete for a common substrate

When two organisms compete for a given substrate without preying on one another, the possible steady states depend on the relative disposition of the two growth curves and the position of the point (Z,θ), whose coordinates are the nutrient feed concentration and dilution rate. It is shown how the stability of each steady state can be understood and qualitative phase portraits can be drawn for each of the 31 distinct types of situations.