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

  • Received: 01 November 2010 Accepted: 29 June 2018 Published: 01 March 2012
  • MSC : Primary: 34D23, 92D25; Secondary: 34D23.

  • 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

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  • 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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