Abstract
In this work, we analyze the existence of discontinuous bifurcation and stability issues in discontinuous flow of bioreactor and membrane reactor models with or without recycle. The reaction is assumed to be governed by certain types of discontinuities in Monod growth kinetics curve leading to discontinuous dynamical system. The criteria for the existence and stability of steady-states of these models are established. More generally, our analysis highlights the presence of several types of bifurcation depending upon the effect of the dilution factor (residence time), biomass concentration and solid-liquid-gas separator efficiency. As well, we present bifurcation conditions defining the dynamics near steady-state branches on the border, providing a possible framework for existing of saddle-node, nonsmooth fold, persistence and grazing-sliding scenarios. It is shown that the critical values of residence time dependence upon recycle ratio, decay rate and existence of discontinuity surface. Further, the performance of the reactor at largest residence times will be discussed. In addition, numerical simulations to illustrate and confirm the results will be carried out.