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|Title:||Applications of dynamical systems to industrial microbiology|
|Department:||Mathematics and Statistics|
|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.|
|Appears in Collections:||Open Access Dissertations and Theses|
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|Meadows_Tyler_A_finalsubmission2019september_PhD.pdf||4.12 MB||Adobe PDF||View/Open|
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