The paper is devoted to a quantitative analysis of the dynamic properties of a cascade of two stirred tank bioreactors, with partial recirculation and thickening of the biomass. Numerical simulation has been carried out for the biodegradation of phenol, with double trophic levels of the type predator-prey, described in terms of the Haldane kinetics. The effects of a mean liquid residence time, initial concentration of the substrate containing carbon and the ratio of the volumes of two bioreactors have been taken into account. The analysis has been done based on the determination of time trajectories, phase portraits and Feigenbaum bifurcation diagrams.