# American Institute of Mathematical Sciences

2012, 9(2): 445-459. doi: 10.3934/mbe.2012.9.445

## Analysis of a model for the effects of an external toxin on anaerobic digestion

 1 Dominican University, 7900 W Division St, River Forest, IL 60305, United States

Received  November 2010 Revised  August 2011 Published  March 2012

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. Mathematical Biosciences & Engineering, 2012, 9 (2) : 445-459. doi: 10.3934/mbe.2012.9.445
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