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A mutualism-parasitism system modeling host and parasite with mutualism at low density
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, United States |
References:
[1] |
, "Agricultural Biogas Casebook," Great Lakes Regional Biomass Energy Program. Available from: http://www.cglg.org/biomass/pub/AgriculturalBiogasCasebook.pdf. |
[2] |
D. J. Batstone, J. Keller, I. Angelidaki, S. Kalyhuzhnyi, S. G. Pavlosthathis, A. Rozzi, W. Sanders, H. Siegrist and V. Vavilin, (IWA Task Group on Modeling Anaerobic Digestion Processes), "Anaerobic Digestion Model No.1 (ADM1)," IWA Publishing, London, UK, 2002. |
[3] |
T. Barkay and I. Wagner-Döbler, Microbial transformations of mercury: Potentials, challenges, and achievements in controlling mercury toxicity in the environment, Adv. Appl. Microbiol., 57 (2005), 1-40.
doi: 10.1016/S0065-2164(05)57001-1. |
[4] |
J. P. Braselton and P. Waltman, A competition model with dynamically allocated inhibitor production, Math. Biosci., 173 (2001), 55-84.
doi: 10.1016/S0025-5564(01)00078-5. |
[5] |
J. D. Bryers, Structured modeling of anaerobic digestion of biomass particulates, Biotechn. Bioeng., 27 (1984), 638-649.
doi: 10.1002/bit.260270514. |
[6] |
G. J. Butler and G. S. K. Wolkowicz, A mathematical model of the chemostat with a general class of functions describing nutrient uptake, SIAM J. Appl. Math., 45 (1985), 138-151.
doi: 10.1137/0145006. |
[7] |
M. Gerardi, "The Microbiology of Anaerobic Digesters,'' Wiley Interscience, Hoboken, 2003.
doi: 10.1002/0471468967. |
[8] |
M. El Hajji, F. Mazenc and J. Harmand, A mathematical study of syntrophic relationship of a model of anaerobic digestion process, Math. Biosci. Eng., 7 (2010), 641-656.
doi: 10.3934/mbe.2010.7.641. |
[9] |
J. Hess and O. Bernard, Design and study of a risk management criterion for an unstable wastewater treatment process, J. of Process Control, 18 (2008), 71-79.
doi: 10.1016/j.jprocont.2007.05.005. |
[10] |
S.-B. Hsu and P. Waltman, A survey of mathematical models of competition with an inhibitor, Math. Biosci., 187 (2004), 53-91.
doi: 10.1016/j.mbs.2003.07.004. |
[11] |
S. Jeyaseelan, A simple mathematical model for anaerobic digestion process, Wat. Sci. Tech., 35 (1997), 185-191.
doi: 10.1016/S0273-1223(97)00166-2. |
[12] |
B. Li, Global asymptotic behaviour of the chemostat: General response function and differential removal rates, SIAM J. Appl. Math., 59 (1999), 411-422.
doi: 10.1137/S003613999631100X. |
[13] |
G. Lyberatos and I. V. Skiadas, Modelling of anaerobic digestion-a review, Global Nest: The Int. J., 1 (1999), 63-76. |
[14] |
L. Markus, Asymptotically autonomous differential systems, in "Contributions to the Theory of Nonlinear Oscillations,'' Princeton University Press, 3, Princeton, NJ, (1953), 17-29. |
[15] |
R. S. Oremland, C. W. Culbertson and M. Winfrey, Methylmercurcy decomposition in sediments and bacterial cultures: Involvement of methanogens and sulfate reducers in oxidative demethylation, Appl. Env. Microbiology, 57 (1991), 130-137. |
[16] |
K. Pak and R. Bartha, Products of mercury demethylation by sulfidogens and methanogens, Bull. Environ. Contam. Toxicol., 61 (1998), 690-694.
doi: 10.1007/s001289900816. |
[17] |
G. E. Powell, Stable coexistence of syntrophic associations in continuous culture, J. Chem. Tech. Biotechnol. B, 35 (1985), 46-50.
doi: 10.1002/jctb.280350109. |
[18] |
H. Smith and P. Waltman, "The Theory of the Chemostat: Dynamics of Microbial Competition,'' Cambridge Studies in Mathematical Biology, 13, Cambridge University Press, Cambridge, 1995. |
[19] |
H. Thieme, Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations, J. of Math. Biology, 30 (1992), 755-763. |
[20] |
G. S. K. Wolkowicz and Z. Lu, Global Dynamics of a mathematical model of competition in the chemostat: General response functions and differential death rates, SIAM J. Appl. Math., 52 (1992), 222-233.
doi: 10.1137/0152012. |
[21] |
L. Zhu, X. Huang and H. Su, Bifurcation for a functional yield chemostat when one competitor produces a toxin, J. Math. Anal. Appl., 329 (2007), 891-903.
doi: 10.1016/j.jmaa.2006.06.062. |
show all references
References:
[1] |
, "Agricultural Biogas Casebook," Great Lakes Regional Biomass Energy Program. Available from: http://www.cglg.org/biomass/pub/AgriculturalBiogasCasebook.pdf. |
[2] |
D. J. Batstone, J. Keller, I. Angelidaki, S. Kalyhuzhnyi, S. G. Pavlosthathis, A. Rozzi, W. Sanders, H. Siegrist and V. Vavilin, (IWA Task Group on Modeling Anaerobic Digestion Processes), "Anaerobic Digestion Model No.1 (ADM1)," IWA Publishing, London, UK, 2002. |
[3] |
T. Barkay and I. Wagner-Döbler, Microbial transformations of mercury: Potentials, challenges, and achievements in controlling mercury toxicity in the environment, Adv. Appl. Microbiol., 57 (2005), 1-40.
doi: 10.1016/S0065-2164(05)57001-1. |
[4] |
J. P. Braselton and P. Waltman, A competition model with dynamically allocated inhibitor production, Math. Biosci., 173 (2001), 55-84.
doi: 10.1016/S0025-5564(01)00078-5. |
[5] |
J. D. Bryers, Structured modeling of anaerobic digestion of biomass particulates, Biotechn. Bioeng., 27 (1984), 638-649.
doi: 10.1002/bit.260270514. |
[6] |
G. J. Butler and G. S. K. Wolkowicz, A mathematical model of the chemostat with a general class of functions describing nutrient uptake, SIAM J. Appl. Math., 45 (1985), 138-151.
doi: 10.1137/0145006. |
[7] |
M. Gerardi, "The Microbiology of Anaerobic Digesters,'' Wiley Interscience, Hoboken, 2003.
doi: 10.1002/0471468967. |
[8] |
M. El Hajji, F. Mazenc and J. Harmand, A mathematical study of syntrophic relationship of a model of anaerobic digestion process, Math. Biosci. Eng., 7 (2010), 641-656.
doi: 10.3934/mbe.2010.7.641. |
[9] |
J. Hess and O. Bernard, Design and study of a risk management criterion for an unstable wastewater treatment process, J. of Process Control, 18 (2008), 71-79.
doi: 10.1016/j.jprocont.2007.05.005. |
[10] |
S.-B. Hsu and P. Waltman, A survey of mathematical models of competition with an inhibitor, Math. Biosci., 187 (2004), 53-91.
doi: 10.1016/j.mbs.2003.07.004. |
[11] |
S. Jeyaseelan, A simple mathematical model for anaerobic digestion process, Wat. Sci. Tech., 35 (1997), 185-191.
doi: 10.1016/S0273-1223(97)00166-2. |
[12] |
B. Li, Global asymptotic behaviour of the chemostat: General response function and differential removal rates, SIAM J. Appl. Math., 59 (1999), 411-422.
doi: 10.1137/S003613999631100X. |
[13] |
G. Lyberatos and I. V. Skiadas, Modelling of anaerobic digestion-a review, Global Nest: The Int. J., 1 (1999), 63-76. |
[14] |
L. Markus, Asymptotically autonomous differential systems, in "Contributions to the Theory of Nonlinear Oscillations,'' Princeton University Press, 3, Princeton, NJ, (1953), 17-29. |
[15] |
R. S. Oremland, C. W. Culbertson and M. Winfrey, Methylmercurcy decomposition in sediments and bacterial cultures: Involvement of methanogens and sulfate reducers in oxidative demethylation, Appl. Env. Microbiology, 57 (1991), 130-137. |
[16] |
K. Pak and R. Bartha, Products of mercury demethylation by sulfidogens and methanogens, Bull. Environ. Contam. Toxicol., 61 (1998), 690-694.
doi: 10.1007/s001289900816. |
[17] |
G. E. Powell, Stable coexistence of syntrophic associations in continuous culture, J. Chem. Tech. Biotechnol. B, 35 (1985), 46-50.
doi: 10.1002/jctb.280350109. |
[18] |
H. Smith and P. Waltman, "The Theory of the Chemostat: Dynamics of Microbial Competition,'' Cambridge Studies in Mathematical Biology, 13, Cambridge University Press, Cambridge, 1995. |
[19] |
H. Thieme, Convergence results and a Poincaré-Bendixson trichotomy for asymptotically autonomous differential equations, J. of Math. Biology, 30 (1992), 755-763. |
[20] |
G. S. K. Wolkowicz and Z. Lu, Global Dynamics of a mathematical model of competition in the chemostat: General response functions and differential death rates, SIAM J. Appl. Math., 52 (1992), 222-233.
doi: 10.1137/0152012. |
[21] |
L. Zhu, X. Huang and H. Su, Bifurcation for a functional yield chemostat when one competitor produces a toxin, J. Math. Anal. Appl., 329 (2007), 891-903.
doi: 10.1016/j.jmaa.2006.06.062. |
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