Analysis of a model for the effects of an external toxin on anaerobic digestion
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...
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AIMS Press
2012-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.445 |
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| author | Marion Weedermann |
| author_facet | Marion Weedermann |
| author_sort | Marion Weedermann |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3b317cd0953141659666b28c45a30ff7 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2012-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-3b317cd0953141659666b28c45a30ff72025-01-24T02:05:30ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-02-019244545910.3934/mbe.2012.9.445Analysis of a model for the effects of an external toxin on anaerobic digestionMarion Weedermann0Dominican University, 7900 W Division St, River Forest, IL 60305Anaerobic 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.https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.445bistability.non-monotone growthchemostatanaerobic digestionglobal stability |
| spellingShingle | Marion Weedermann Analysis of a model for the effects of an external toxin on anaerobic digestion Mathematical Biosciences and Engineering bistability. non-monotone growth chemostat anaerobic digestion global stability |
| title | Analysis of a model for the effects of an external toxin on anaerobic digestion |
| title_full | Analysis of a model for the effects of an external toxin on anaerobic digestion |
| title_fullStr | Analysis of a model for the effects of an external toxin on anaerobic digestion |
| title_full_unstemmed | Analysis of a model for the effects of an external toxin on anaerobic digestion |
| title_short | Analysis of a model for the effects of an external toxin on anaerobic digestion |
| title_sort | analysis of a model for the effects of an external toxin on anaerobic digestion |
| topic | bistability. non-monotone growth chemostat anaerobic digestion global stability |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.445 |
| work_keys_str_mv | AT marionweedermann analysisofamodelfortheeffectsofanexternaltoxinonanaerobicdigestion |