Modeling phytoplankton dynamics using catastrophe theory

Abstract

The use of catastrophe theory to obtain a predictive model of the eutrophication phenomenon is examined and applied to the case of small, highly eutrophic ponds or embayments in large water bodies. Phytoplankton dynamics is represented by a non‐linear differential equation derived on the basis of phenomenological considerations. This equation can be reduced analytically to the canonical form for a cusp catastrophe model. Numerical integration of the dynamics equation is calibrated with data taken during a phytoplankton bloom in small ponds by Parks et al. (1975). The model trajectory matches closely the data for both Anabaena concentrations and total algae concentration; however, model trajectory for a third variable, solution phosphate concentration, appears to match laboratory data rather than field observations. Implications for fish pond management are given, and possible use of the catastrophe theory approach to model algal succession is discussed.