Microbial growth in periodic gradostats
A gradostat is a laboratory device with which one can study the growth of microorganisms in a nutrient gradient. As constructed by \textit{R. W. Lovitt} and \textit{J. W. T. Wimpenny} [Soc. Gen. Microbial Quart. 6 (1979)] a gradostat is a concatenation of several chemostats in which adjacent vessels are connected by tubes allowing pumps to exchange the material contents of each vessel. The aim of the paper is to study a mathematical model of the growth of a single species of microorganisms in the presence of one limiting substrate or two limiting complementary substrates in a very general gradostat where essentially arbitrary connections between vessels are allowed. In addition, we allow operating parameters such as flow rates and reservoir nutrient concentration to vary periodically in time, simulating seasonal or diurnal variations in natural environments. The mathematical model reduces to a system of periodic, nonautonomous quasimonotone ordinary differential equations for species concentration in each vessel. The extinction or persistence of the population in the gradostat is determined by whether a certain dominant Floquet multiplier of a known quasimonotone linear periodic system either does not or does exceed unity. If the multiplier exceeds one then all nontrivial solutions are shown to approach a unique periodic steady state oscillation.
system of periodic, nonautonomous quasimonotone ordinary differential equations
scientific article; zbMATH DE number 4200042
scientific article