Dynamic behavior of double-substrate interactive model

Although modeling microbial growth with one limiting substrate such as Monod model is a common practice, microbes very often consume multiple substances from the environment for their growth. Therefore, the extension of current model to a multi-substrate analysis is needed for practical applications. The dynamic behavior of a double-substrate interactive growth model with Andrew's substrate inhibition model is theoretically discussed in this article. The yield factors considered are either a constant or a linear function of limiting substrate. The simulation indicated that there could be at least three non-trivial steady-state solutions with similar dynamic behavior for all the three cases, i.e. substrate without inhibition, one or both substrate with inhibition. The steady state of highest productivity is always a stable one. The steady state of the lowest productivity could change from a stable mode to an unstable mode while increasing dilution rate. And the limit cycle (sustained oscillation) could appear during the transition. The other steady state is always unstable. For the cases of one or both limiting substrates inhibition, the fourth steady state could appear, and it is always unstable.