Anaerobic digestion has been modeled as a two-stage process using coupled chemostat models with non-monotone growth functions, [9].
This study incorporates the effects of an external toxin. After reducing the model to a 3-dimensional system, global stability
of boundary and interior equilibria is proved using differential inequalities and comparisons to the corresponding toxin-free model.
Conditions are given under which the behavior of the toxin-free model is preserved. Introduction of the toxin results in additional patterns such as
bistabilities of coexistence steady states or of a periodic orbit and an interior steady state.
Citation: Marion Weedermann. Analysis of a model for the effects of an external toxin on anaerobic digestion[J]. Mathematical Biosciences and Engineering, 2012, 9(2): 445-459. doi: 10.3934/mbe.2012.9.445
Abstract
Anaerobic digestion has been modeled as a two-stage process using coupled chemostat models with non-monotone growth functions, [9].
This study incorporates the effects of an external toxin. After reducing the model to a 3-dimensional system, global stability
of boundary and interior equilibria is proved using differential inequalities and comparisons to the corresponding toxin-free model.
Conditions are given under which the behavior of the toxin-free model is preserved. Introduction of the toxin results in additional patterns such as
bistabilities of coexistence steady states or of a periodic orbit and an interior steady state.