Mathematical investigations of growth of microorganisms in the gradostat
The author investigates analytically and numerically the growth of a single species of microorganisms in the gradostat, finding that the growth can be described by a mathematical model similar to that one for the chemostat, assuming Michaelis-Menten kinetics of uptake of substrate by the microorganisms. The model for the cases where there is a gradient of one limiting substrate, and where there are opposing gradients of two limiting complementary substrates is a system of 2n and, respectively, 3n equations - n being the number of vessels. The solutions of the system of nonlinear algebraic equations are considered as fixed points of an operator in an ordered Banach space, and the global bifurcation from the trivial solution is studied. The nontrivial solution is obtained numerically and qualitatively analyzed. The expectation that concentrations of the microorganisms are maximum close to the source and decreasing gradually along the series of vessels is confirmed if the parameters are not close to the bifurcation values. On the contrary, when there are two limiting complementary substrates in opposing gradients, microorganisms concentrate most in the middle of the gradostat, only if the parameters are close to the bifurcation values. The analysis shows that growth of microorganisms in the gradostat does not depend on their initial concentration, the transport between the vessels having a significant effect on the growth rate. Thus, different transport rates give different asymptotic behaviours.
scientific article; zbMATH DE number 3976850
scientific article