PIMS—UManitoba Distinguished Lecture: Gail Wolkowicz

A video of this event is available on mathtube.org

Anaerobic digestion is a complex, naturally occurring process during which organic matter is broken down into biogas and various byproducts in an oxygen-free environment. It is used for bioremediation and the production of methane which can be used to produce energy from animal waste. A system of differential equations modelling the interaction of microbial populations in a chemostat is used to describe three of the four main stages of anaerobic digestion: acidogenesis, acetogenesis, and methanogenesis. To examine the effects of the various interactions and inhibitions, we study both an inhibition-free model and a model with inhibition.

A case study illustrates the importance of including inhibition on the regions of stability. Implications for optimizing biogas production are then explored. In particular, which control parameters and changes in initial conditions the model predicts can move the system to, or from, the optimal state are then considered. An even more simplified model proposed in Bornh\”{o}ft, Hanke-Rauschenback, and Sundmacher [Nonlinear Dynamics 73, 535-549 (2013)], claimed to capture most of the qualitative dynamics of the process is then analyzed. The proof requires considering growth in the chemostat in the case of a general class of response functions including non-monotone functions when the species death rate is included.