Applications of dynamical systems to industrial microbiology

Abstract

The use of microorganisms in industrial processes has become very common. In this thesis, we analyze three models of such systems that have applications in green technology. The first is a simplified model of anaerobic digestion, originally introduced as a qualitative simplification of the anaerobic digestion model no 1 (ADM1). While ADM1 is very complicated, the simplified model is composed of only five ordinary differential equations. We show that this model can be reduced to a two-dimensional system that is equivalent to the basic chemostat model with explicit species death rate and non-monotone response function. We show that this chemostat model has no periodic solutions and completely characterize the possible dynamics of the two dimensional system and then the full five-dimensional system. In the second model, we consider the self-cycling fermentation process with two limiting essential resources with impulses that occur when both resources fall below a prescribed threshold. We show that the successful operation of the self-cycling fermentor is initial-condition dependent and that success is equivalent to the convergence of solutions to a periodic solution. We show numerically that there is an optimal choice for the emptying/refilling fraction and that the optimal choice is not always 1/2, the standard choice in the engineering literature. In the third model, we consider the self-cycling fermentation process with an arbitrary number of nutrients with impulses that occur when one specified nutrient concentration falls below a prescribed threshold. We show that successful operation of the self-cycling fermentor is equivalent to the convergence of solutions to a periodic solution. We derive conditions for the existence of this periodic solution and initial-condition-dependent conditions for convergence to this solution.