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| We present a model for anaerobic digestion, a complex naturally occurring process during which organic matter is broken down to biogas and various byproducts in an oxygen-free environment. In waste treatment facilities the biogas is captured before it escapes into the atmosphere and can then be used as renewable energy. The model consists of differential equations describing the interactions of microbial populations involved in three of the four main stages of anaerobic digestion: acidogenesis, acetogenesis, and methanogenesis. Due to various inhibitory effects, the system possesses regions of bistability in parameter space. We argue that the highest biogas production is achieved in regions where control parameters are likely to give a bistable state. Surprisingly, the optimal biogas production does not always occur at a steady state where all the different classes of microorganisms coexist. In some regions of bistability biogas production occurs at only one of the steady states, while in others both steady-states result in biogas production with one state being more productive than the other. We show which control parameters and changes in initial conditions can move the system to or from the optimal state. |
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