In this thesis I analyse mathematical models for an ideal and non-ideal bioreactor. The differences between these models are that in the ideal bioreactor model mixing is assumed to be perfect whereas in the non-ideal bioreactor model the mixing is not assumed to be perfect.
The model for the ideal bioreactor is represented by a system of two non-linear ordinary differential equations. For the ideal reactor model we found the steady-state solutions and determined their stability as a function of the residence time, which si the main experimental control parameter.
The model for the non-ideal bioreactor is given by a system of four non-linear ordinary differential equations. For the non-ideal reactor model we found some of the steady-state solutions and determined the stability of the washout branch. Even though we were not able to finish the analysis we still found some interesting results about how incomplete mixing affects the performance of the reactor.
The interaction between the predator and prey in both models is assumed to be governed by the well-known Monod growth kinetics. The main application of work considered here is to the biological treatment of industrial wastewater.