Equilibria, stability and excitability in a general class of plankton population models

Abstract

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 phytoplankton growth rate such as nutrient shortage and self-shading were represented parametrically. Here, we demonstrate the relationship of such a two-component system to a general class of three-component models in which nutrient is more realistically regarded as a third evolving variable, and self-shading is included as a growth rate modulation. We derive conditions for the existence and stability of equilibrium states which are generally valid for this class, and interprete the behaviour of particular models, proposed elsewhere, within this picture.