Persistence in variable-yield nutrient-plankton models

Nutrient-phytoplankton-zooplankton models with general uptake functions in which only the internal nutrient concentration is capable of catalyzing cell growth and division for phytoplankton are proposed and analyzed. For the constant nutrient input model, it is shown that extinction or persistence of the population depends on its maximal growth rate relative to the total removal rate. The same biological conclusions hold for the periodic nutrient input model. However, while extinction and persistence are expressed in terms of convergence to steady states for the constant nutrient input model, these biological phenomena are exhibited in terms of asymptotic attraction to periodic solutions for the periodic nutrient input model.