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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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