Search Advanced

Mathematical Biosciences and Engineering

2012, Volume 9, Issue 2: 445-459. doi: 10.3934/mbe.2012.9.445
Previous Article Next Article

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
  • 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

    Related Papers:

    [1] Tewfik Sari, Miled El Hajji, Jérôme Harmand . The mathematical analysis of a syntrophic relationship between two microbial species in a chemostat. Mathematical Biosciences and Engineering, 2012, 9(3): 627-645. doi: 10.3934/mbe.2012.9.627
    [2] Boumediene Benyahia, Tewfik Sari . Effect of a new variable integration on steady states of a two-step Anaerobic Digestion Model. Mathematical Biosciences and Engineering, 2020, 17(5): 5504-5533. doi: 10.3934/mbe.2020296
    [3] Andrés Donoso-Bravo, Pedro Gajardo, Matthieu Sebbah, Diego Vicencio . Comparison of performance in an anaerobic digestion process: one-reactor vs two-reactor configurations. Mathematical Biosciences and Engineering, 2019, 16(4): 2447-2465. doi: 10.3934/mbe.2019122
    [4] Daniele Bernardo Panaro, Andrea Trucchia, Vincenzo Luongo, Maria Rosaria Mattei, Luigi Frunzo . Global sensitivity analysis and uncertainty quantification for a mathematical model of dry anaerobic digestion in plug-flow reactors. Mathematical Biosciences and Engineering, 2024, 21(9): 7139-7164. doi: 10.3934/mbe.2024316
    [5] Miled El Hajji, Frédéric Mazenc, Jérôme Harmand . A mathematical study of a syntrophic relationship of a model of anaerobic digestion process. Mathematical Biosciences and Engineering, 2010, 7(3): 641-656. doi: 10.3934/mbe.2010.7.641
    [6] Amer Hassan Albargi, Miled El Hajji . Mathematical analysis of a two-tiered microbial food-web model for the anaerobic digestion process. Mathematical Biosciences and Engineering, 2023, 20(4): 6591-6611. doi: 10.3934/mbe.2023283
    [7] Jianquan Li, Zuren Feng, Juan Zhang, Jie Lou . A competition model of the chemostat with an external inhibitor. Mathematical Biosciences and Engineering, 2006, 3(1): 111-123. doi: 10.3934/mbe.2006.3.111
    [8] Toshikazu Kuniya, Tarik Mohammed Touaoula . Global stability for a class of functional differential equations with distributed delay and non-monotone bistable nonlinearity. Mathematical Biosciences and Engineering, 2020, 17(6): 7332-7352. doi: 10.3934/mbe.2020375
    [9] Tewfik Sari, Frederic Mazenc . Global dynamics of the chemostat with different removal rates and variable yields. Mathematical Biosciences and Engineering, 2011, 8(3): 827-840. doi: 10.3934/mbe.2011.8.827
    [10] Patrick De Leenheer, Martin Schuster, Hal Smith . Strong cooperation or tragedy of the commons in the chemostat. Mathematical Biosciences and Engineering, 2019, 16(1): 139-149. doi: 10.3934/mbe.2019007
  • 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.


  • This article has been cited by:

    1. Marion Weedermann, Gunog Seo, Gail Wolkowicz, Mathematical model of anaerobic digestion in a chemostat: effects of syntrophy and inhibition, 2013, 7, 1751-3758, 59, 10.1080/17513758.2012.755573
    2. Marion Weedermann, Gail S. K. Wolkowicz, Joanna Sasara, Optimal biogas production in a model for anaerobic digestion, 2015, 81, 0924-090X, 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, 2014, 20, 14681218, 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, 2018, 302, 00255564, 27, 10.1016/j.mbs.2018.05.004
    5. Sarra Nouaoura, Radhouane Fekih-Salem, Nahla Abdellatif, Tewfik Sari, Mathematical analysis of a three-tiered food-web in the chemostat, 2020, 0, 1553-524X, 0, 10.3934/dcdsb.2020369
    6. Sarra Nouaoura, Radhouane Fekih-Salem, Nahla Abdellatif, Tewfik Sari, Operating diagrams for a three-tiered microbial food web in the chemostat, 2022, 85, 0303-6812, 10.1007/s00285-022-01812-5
    7. Tewfik Sari, Commensalism and syntrophy in the chemostat: a unifying graphical approach, 2024, 9, 2473-6988, 18625, 10.3934/math.2024907
  • Reader Comments
  • © 2012 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
4.4

Metrics

Article views(2710) PDF downloads(535) Cited by(7)

Preview PDF
Download XML
Export Citation
Article outline
Abstract

Other Articles By Authors

Related pages

Tools

Copyright © AIMS Press

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog