EQUILIBRIA, STABILITY AND EXCITABILITY IN A GENERAL-CLASS OF PLANKTONPOPULATION-MODELS

In a recent paper we proposed a simple ODE model for the behaviour of populations of phytoplankton and zooplankton which had a mathematical structure analogous to models of excitable media. That model comprised a two-component system, in which limiting effects on the phytoplankto n growth rate such as nutrient shortage and self-shading were represen ted parametrically. Here, we demonstrate the relationship of such a tw o-component system to a general class of three-component models in whi ch nutrient is more realistically regarded as a third evolving variabl e, and self-shading is included as a growth rate modulation. We derive conditions for the existence and stability of equilibrium states whic h are generally valid for this class, and interprete the behaviour of particular models, proposed elsewhere, within this picture.