Section: Application Domains
Control of continuous bioreactors
We study problems of coexistence or regulation of species of micro-organisms in bio-reactors called chemostats.
In  , we have studied a competition model between an arbitrary number of species in a chemostat with one limiting substrate and including both monotone and non-monotone growth functions, distinct removal rates and variable yields. The dilution rate and the substrate input concentration were chosen as positive constants. We have shown that only the species with the lowest break-even concentration survives, provided that additional technical conditions on the growth functions and yields are satisfied. The proof relies on the construction of a Lyapunov function
In  , we studied chemostat models in which the species compete for two or more limiting substrates. First we considered the case where the nutrient flow and species removal rates and input nutrient concentrations are all given positive constants. In that case, we use Brouwer degree theory to give conditions guaranteeing that the models admit globally asymptotically stable componentwise positive equilibrium points, from all componentwise positive initial states. Then we used the results to develop stabilization theory for controlled chemostats with two or more limiting nutrients. For cases where the dilution rate and input nutrient concentrations can be selected as controls, we prove that many different componentwise positive equilibria can be made globally asymptotically stable. This significantly extends the existing control results for chemostats with one limiting nutrient. We demonstrate our methods in simulations.