Regime shifts in eutrophied lakes: a mathematical study

In this article, a two dimensional coupled differential system is constructed to represent the dynamics of a lake exposed to eutrophication. The aim is to throw some light on the flipping behaviour associated with the lakes by incorporating vital nonlinear interactions between the phosphorus in water and sediments in a simple model. This model reveals important general patterns observed with the lake ecosystems. It explains the surprising dynamics of eutrophied lakes like regime shifts and the reasons for cyclic behaviour observed during the management of lakes, which are not explained by the existing models. The analysis identifies strategies to break away from the cyclic behaviour during the lake management. A necessity to increase the dimension of the model in order to explain the dynamics in irreversible lakes, in which eutrophication cannot be reversed even by severe reductions in the phosphorus input, has been highlighted. Several modifications are suggested to increase the realism of the model and for further contribution.