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

Marion Weedermann

doi:10.3934/mbe.2012.9.445

Article Contents

2012, Volume 9, Issue 2: 445-459. Doi: 10.3934/mbe.2012.9.445

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

Marion Weedermann^1,

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

Received: October 31, 2010

Revised: July 31, 2011

Published: February 2012

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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.

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Mathematics Subject Classification: Primary: 34D23, 92D25; Secondary: 34D23.

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