Glycolysis in Trypanosoma brucei was modeled using a reaction transport simulator and tested for possible complex dynamics. The glycolytic model is multi-compartmentalized and accounts for the exchange of metabolites between the glycosomes, cytosol, mitochondrion and the host medium. The model is used to examine the effects of a range of culture medium concentrations of oxygen on the glycolysis of T. brucei. Our results are in good agreement with steady-state experiments. We also find that under aerobic conditions, increasing the activity of glycerol-3-phosphate dehydrogenase induces complex dynamics in the system. We report the presence of three distinct types of these dynamics. Varying the oxygen concentration in the medium can induce the transition between these dynamics.