Open AccessAnalysis of a model for the effects of an external toxin on anaerobic digestion
Author(s) -
Marion Weedermann
Publication year - 2012
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2012.9.445
Subject(s) - chemostat , steady state (chemistry) , toxin , monotone polygon , stability (learning theory) , boundary (topology) , mathematics , monotonic function , anaerobic digestion , boundary value problem , biological system , control theory (sociology) , mechanics , physics , chemistry , mathematical analysis , computer science , biology , ecology , methane , biochemistry , geometry , genetics , control (management) , machine learning , artificial intelligence , bacteria
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.