Mathematical models of nutrient recycling and toxin production in a gradostat

We discuss several gradostat models in which a microbial population excretes a dissolved toxin, which in some cases can get recycled back into the system as a nutrient source. Each mathematical model consists of six ordinary differential equations and represents the dynamics of harmful algal blooms in a two compartment gradostat, for example representing lakes with fringing coves. We examine three different modes of toxin production, related to the algal growth rate, mortality rate, and nutrient limitation, respectively. Local and global stability analysis of the equilibria predict that algal abundance and toxin concentration can be both washed out or both persist under different environmental conditions. All theoretical results are supported by a set of numerical simulations.