A three dimensional chemostat with quadratic yields (Q2503699)

The paper deals with a model of a chemostat with two microorganisms, in which the yield functions are considered to be quadratic in the concentration of the nutrient. The authors use qualitative analysis and bifurcation theory to discuss the existence and stability of the equilibrium points, the existence of limit cycles, the Hopf bifurcation and the existence of a positive invariant set for the system of equations describing the model. They also prove that if there exists an asymptotically stable equilibrium point, then one can find at least two limit cycles around it.