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Chemostats with Time-Dependent Inputs and Wall Growth |
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PP: 2283-2296 |
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Author(s) |
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Tomás Caraballo,
Xiaoying Han,
Peter Kloeden,
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Abstract |
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| Traditional assumptions in the simple chemostat model include fixed availability of the nutrient and its supply rate, and
fast flow rate to avoid wall growth. However, these assumptions become unrealistic when the availability of a nutrient depends on the
nutrient consumption rate and input nutrient concentration and when the flow rate is not fast enough. In this paper, we relax these
assumptions and study the chemostat models with a variable nutrient supplying rate or a variable input nutrient concentration, with
or without wall growth. This leads the models to nonautonomous dynamical systems and requires new concepts of nonautonomous
attractors from the recently developed theory of nonautonomous dynamical systems. Our results provide sufficient conditions for
existence of nonautonomous attractors and singleton attractors. |
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