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In this work, we consider a gradostat made up of several chemostats coupled by migrations of substrates and products between them. We seek maximum product synthesis or maximum sustainable yield by optimizing with the dilution rate. The mathematical study of the complete model is carried out by searching equilibrium points and stability. We compare the overall maximal synthesis of the system of coupled chemostats to the sum of the maximal syntheses of isolated chemostats. We show that in the homogeneous case where all the chemostats are identical, the difference between the maximum synthesis of the system of coupled chemostats and the sum of the maximum syntheses of the isolated chemostats or excess yield cannot be positive. We show that the excess yield can be positive only in the heterogeneous case. In these cases, under some conditions, the coupling of chemostats can make it possible to obtain a higher productivity compared to the case of isolated chemostats. We illustrate our theoretical results with numerical simulations with various examples corresponding to slow and fast migrations.

This paper considers the production of biomass of two interconnected chemostats in series with biomass mortality and a growth kinetic of the biomass described by an increasing function. A comparison is made with the productivity of a single chemostat with the same mortality rate and with volume equal to the sum of the volumes of the two chemostats. We determine the operating conditions under which the productivity of the serial configuration is greater than the productivity of the single chemostat. Moreover, the differences and similarities in the results corresponding to the case with mortality and the one without mortality, are highlighted. The mortality leads to surprising results where the productivity of a steady state where the bacteria are washed out in the first chemostat is greater than the one where the bacteria are present in both chemostats.