Three variable marine ecosystems models: A simple geometrical approach

A three variable model which has an exact solution is examined. The three variables can be interpreted to be an omnivore (Zooplankton), a herbivore (phytoplankton) and a food source (nutrient). Mathematically, the solution is shown to lie on the surface of a torus. Choices in both the formulation of the differential equations and variations of the geometric parameters of the torus allow an interesting variety of model situations. We also investigate the existence of attractors and repellors in these models, and some consequences to the ecosystems they represent.