Competition in the bioreactor with general quadratic yields when one competitor produces a toxin |
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Authors: | Xuncheng Huang Yuanming Wang Lemin Zhu |
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Institution: | (1) Yangzhou Polytechnic University, Yangzhou, Jiangsu, 225012, P.R. China;(2) Present address: 12A-903 Hao Yue Yuan, Moon Park, Yangzhou, Jiangsu, 225012, China |
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Abstract: | Microorganisms produce toxins against its competitors sometimes, and variable yields are useful to explain the observed oscillatory
behavior in the reactor. In this paper, a model with general quadric yields of competition in the bioreactor of two competitors
for a single nutrient where one of the competitors can produce toxin against its opponent, is proposed. We analyze the asymptotic
behavior of the model in terms of the relevant parameters. The conditions of the three dimensional Hopf bifurcation, and the
existence of limit cycles in the nutrient-organism phase plane are obtained. |
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Keywords: | bioreactor quadratic yields toxin Hopf bifurcation limit cycles |
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