Global stability in chemostat-type plankton models with delayed nutrient recycling
This paper considers chemostat-type plankton models with delays, and proves global attractivity of the positive equilibrium in the following cases: delays in the nutrient recycling, first of all, a continuous delay, with a fading memory term, then a discrete constant and finally a discrete variable delay; delays in both the nutrient recycling and the growth response. Proofs are done by setting up integral expressions involving the state variables, and finding sufficient conditions in terms of the average time delay under which these expressions are Lyapunov functionals. A thorough introduction presents arguments, gathered from the literature, regarding the type of model considered in the paper (the Monod model is chosen here rather than the Droop model) and also the importance of delay in systems with nutrient recycling. Finally, comparisons are made with the literature, notably with work by E. Beretta and coworkers.
scientific article; zbMATH DE number 1211564