Premium
Modeling phytoplankton dynamics using catastrophe theory
Author(s) -
Duckstein Lucien,
Casti John,
Kempf James
Publication year - 1979
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1029/wr015i005p01189
Subject(s) - catastrophe theory , eutrophication , phytoplankton , trajectory , environmental science , algal bloom , differential equation , ecology , mathematics , physics , geology , mathematical analysis , biology , geotechnical engineering , astronomy , nutrient
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.