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

Primary: 34D23, 92D25; Secondary: 34D23.

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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

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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Keywords bistability.; non-monotone growth; chemostat; Anaerobic digestion; global stability

Citation: Marion Weedermann. Analysis of a model for the effects of an external toxin on anaerobic digestion. Mathematical Biosciences and Engineering, 2012, 9(2): 445-459. doi: 10.3934/mbe.2012.9.445

 

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  • 2. Marion Weedermann, Gail S. K. Wolkowicz, Joanna Sasara, Optimal biogas production in a model for anaerobic digestion, Nonlinear Dynamics, 2015, 81, 3, 1097, 10.1007/s11071-015-2051-z
  • 3. Hua Nie, Na Liu, Jianhua Wu, Coexistence solutions and their stability of an unstirred chemostat model with toxins, Nonlinear Analysis: Real World Applications, 2014, 20, 36, 10.1016/j.nonrwa.2014.04.002
  • 4. Mohamed Dellal, Mustapha Lakrib, Tewfik Sari, The operating diagram of a model of two competitors in a chemostat with an external inhibitor, Mathematical Biosciences, 2018, 10.1016/j.mbs.2018.05.004

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