Agenda

Abstract: In this talk, we will introduce a system of two coupled reaction-diffusion PDEs modeling phytoplankton-nutrient dynamics in an oceanic environment and for a single phytoplankton species depending on a single nutrient (and light) for its survival. In the
first half of this talk, we will look closely into the linear stability problem for the trivial steady state (no phytoplankton) and use this asymptotic analysis to identify the emergence of localized structures. These turn out to fall into two categories: deep-chlorophyll maxima, in which the plankton concentration is localized in an interior point of the water column, and benthic
layers, in which the plankton concentration is localized in the bottom of the column. This first half will close with a brief ecological interpretation of our findings. In the second half, we
will look into the weakly nonlinear stability problem for the bifurcating deep-chlorophyll maxima. The peculiarity of this problem is focused around the existence of an infinite number of latent (non-bifurcating) modes which invariably have to be included in the analysis. Explicit asymptotic results may nevertheless be derived, not only close to the bifurcation point, but in a far bigger regime. In fact, the talk will conclude with the deep-chlorophyll maximum
disappearing in a saddle-node bifurcation, thus offering its place to a secondary pattern.