### Analysis of chemostat models with application to a model of anaerobic digestion

#### Abstract

The talk will begin by providing a short, apparently overlooked, proof of competitive exclusion for a model of n-species competition in the chemostat when maintenance is ignored [3]. Then a simpliﬁed model of anaerobic digestion will be considered. Anaerobic digestion is a complex naturally occurring process used for waste and wastewater treatment to produce biogas as a renewable source of energy. The so-called Anaerobic Digestion Model No. 1 (ADM1) in [1] includes 32 state variables and is not mathematically tractable. Bornh oft et al. [2] proposed a simpliﬁed model that seems to capture most of the qualitative dynamics of the ADM1 model, including the possibility of bi-stability and the bifurcation dynamics when substrate concentration is used as the bifurcation parameter. Our analysis shows that not all of the dynamics possible in ADM1 are captured. Our analysis of this model also required studying a chemostat model without ignoring the maintenance term for a general class of response functions, that includes nonmonotone functions, that had not been analyzed. I will provide a proof in this case for competition between two populations using the Lyapunov function introduced in [4]. The talk will conclude with a consideration of the sensitivity of the predictions of the model to stochastic perturbations,and a discussion of the implications of the model predictions for successful operation of the process of anaerobic digestion.

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PDF#### References

D. Batstone, J. Keller, I. Angelidaki, S. Kalyhuzhnyi, S. Pavlosthathis, A. Rozzi, W. Sanders, H. Siegrist, and V. Vavilin, Anaerobic Digestion Model No.1 (ADM1), IWA Publishing, London UK, 2002

A. Bornhoft, R. Hanke-Rauschenbach, and K. Sundmacher, Steady-state analysis of the anaerobic digestion model no.1 (ADM1), Nonlinear Dynamics, 73, 535-549, 2013

Butler, G. J. 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, 138-151, 1985

G. S. W. Wolkowicz and Z. Lu, Global Dynamics of a mathematical model of competition in the chemostat: general response function and differential death rates, SIAM Journal on Applied Mathematics, 52, 222-233, 1992

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