Catastrophic shifts in vertical distributions of phytoplankton: the existence of a bifurcation set.
A model of phytoplankton dynamics within a water column was analyzed with special consideration on the existence of a bifurcation set in the parameter space. We considered two resources, light and a limiting nutrient, for phytoplankton growth and assumed that the water column is separated into two layers by thermal and/or density stratification. It was shown that there exists a bifurcation set in the parameter space when the growth function meets several conditions that are general for growth functions of two essential resources. Specifically, these conditions include that a less abundant of the two resources limits the growth while the effect of the other is sufficiently small. Folded structure with two stable states separated by one unstable state appears in the catastrophe manifold when parameters move to a certain direction with a certain curvature from a point in the bifurcation set. These results suggest that occurrence of discontinuous transition between two alternative vertical patterns is possible nature of phytoplankton dynamics within a stratified water column.