
Mathematical Biosciences and Engineering, 2020, 17(5): 62176239. doi: 10.3934/mbe.2020329
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Competitive exclusion in a DAE model for microbial electrolysis cells
1 Department of Applied Mathematics, University of Colorado, Boulder, CO 803090526, USA
2 Department of Civil and Environmental Engineering, Princeton University, Princeton, NJ 08544, USA
Received: , Accepted: , Published:
Special Issues: Recent advances of mathematical modeling and computational methods in cell and developmental biology
We show that if methanogens can grow at the lowest substrate concentration, then the equilibrium corresponding to competitive exclusion by methanogens is globally asymptotically stable. The analogous result for electroactive bacteria is not necessarily true. In fact we show that local asymptotic stability of competitive exclusion by electroactive bacteria is not guaranteed, even in a simplified version of the model. In this case, even if electroactive bacteria can grow at the lowest substrate concentration, a few additional conditions are required to guarantee local asymptotic stability. We provide numerical simulations supporting these arguments. Our results suggest operating conditions that are most conducive to success of electroactive bacteria and the resulting current and hydrogen production in MECs. This will help identify when producing methane or electricity and hydrogen is favored.
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