Global dynamics of the buffered chemostat for a general class of response functions

Abstract

We study how a particular spatial structure with a buffer impacts the number of equilibria and their stability in the chemostat model. We show that the occurrence of a buffer can allow a species to persist or on the opposite to go extinct, depending on the characteristics of the buffer. For non-monotonic response functions, we characterize the buffered configurations that make the chemostat dynamics globally asymptotically stable, while this is not possible with single, serial or parallel vessels of the same total volume and input flow. These results are illustrated with the Haldane kinetic function.

Performance Study of Two Serial Interconnected Chemostats with Mortality

“…The performance is considered for different criteria studied in the literature [31], among which the most common are: the output substrate concentration, the residence time, the biogas flow rate and the biomass productivity. Particular interconnection structures have been investigated and compared for the properties in terms of input-output performances (see for instance [5,7,15,28]). It has been notably shown that a series of reactors instead of a single perfectly mixed one can significantly improve the performances of the bioprocess (in terms of matter conversion) while preserving the same residence time, or equivalently that the same performance can be obtained with a smaller residence time considering several tanks in series instead of a single one [14,17,24,25,47].…”

Some non-intuitive properties of simple extensions of the chemostat model

“…For such cases, there is a unique positive equilibrium in the first tank as well. In [37], the following result is given.…”

“…It has been shown in [37] that the graphs of the family of functions φ r (·) for r ∈ (0, 1) have the point (s 1 , D) in common, wheres 1 = αs 2 + (1 − α)S in . there always exist functions φ r (·) whose graph possesses a unique intersection with the graph of µ(·).…”

“…One can also see on Figure 7 that the price to pay for stability with a buffered 235 interconnection is that the output concentration of the resource s out as steady state (which is equal to s 1 ) is larger than λ − (D), which is the output concentration of the single chemostat of volume V at the positive equilibrium. In [37], the problem of minimizing s out among all the buffered configurations that ensure global stability is also studied. The following result is provided in [37].…”

“…In [37], the problem of minimizing s out among all the buffered configurations that ensure global stability is also studied. The following result is provided in [37]. 2.…”