Seasonality and Chaos in a Plankton Fish Model

The dynamics of a plankton-fish model comprising phosphorus, algae, zooplankton and young fish are analyzed for different values of average light intensity, phosphorus concentration in the inflow, and adult fish biomass. Light intensity and water temperature are periodically varied during the year, while the other parameters are fixed at realistic values. The analysis is carried out with a continuation method for the study of the bifurcations of periodically forced continuous-time nonlinear systems. The large number of bifurcations of different types indicates that the dynamics of the model can be very complex. In fact, multiplicity of attractors, catastrophic transitions, subharmonics of various periods, cascades of period doublings, and strange attractors arise for suitable values of the parameters. The results are in agreement with the most recent theories on food chain systems and periodically forced predator-prey systems. They also suggest that large year-to-year differences in food chain dynamics need not always be attributable to external factors like interannual weather variability.