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Book Sections Year : 2015

Dynamics of Nonautonomous Chemostat Models

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Abstract

Chemostat models have a long history in the biological sciences as well as in biomathematics. Hitherto most investigations have focused on autonomous systems, that is, with constant parameters, inputs, and outputs. In many realistic situations these quantities can vary in time, either deterministically (e.g., periodically) or randomly. They are then nonautonomous dynamical systems for which the usual concepts of autonomous systems do not apply or are too restrictive. The newly developing theory of nonautonomous dynamical systems provides the necessary concepts, in particular that of a nonautonomous pullback attractor. These will be used here to analyze the dynamical behavior of nonautonomous chemostat models with or without wall growth, time-dependent delays, variable inputs and outputs. The possibility of overyielding in nonautonomous chemostats will also be discussed.

Dates and versions

hal-01162471 , version 1 (10-06-2015)

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Cite

Tomas Caraballo, Xiaoying Han, Peter Kloeden, Alain Rapaport. Dynamics of Nonautonomous Chemostat Models. Sadovnichiy, Viktor A.; Zgurovsky, Mikhail Z. Continuous and Distributed Systems Theory and Applications Part II, 30, Springer, pp.103-120, 2015, Studies in Systems, Decision and Control, 978-3-319-19074-7. ⟨10.1007/978-3-319-19075-4_6⟩. ⟨hal-01162471⟩
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