Mathematical analysis of a chemostat system modeling the competition for light and inorganic carbon with internal storage

This paper investigates a mathematical model of competition between two species for inorganic carbon and light in a well-mixed water column. The population growth of the species depends on the consumption of two substitutable forms of inorganic carbon, "CO2" (dissolved CO2 and carbonic acid) and "CARB" (bicarbonate and carbonate ions), which are stored internally. Besides, uptake rates also includes self-shading by the phytoplankton population, that is, an increase in population density will reduce light available for photosynthesis, and thereby reducing further carbon assimilation and population growth. We also incorporate the fact that carbon is lost by respiration, and the respiration rate is assumed to be proportional to the size of the transient carbon pool. Then we study the extinction and persistence of a single-species system. Finally, we show that coexistence of the two-species system is possible, depending on parameter values, and both persistence of one population.