  Co-limitation of marine phytoplankton growth by light and nutrient, both of
which are essential for phytoplankton, leads to complex dynamic behavior and a
wide array of coherent patterns. The building blocks of this array can be
considered to be deep chlorophyll maxima, or DCMs, which are structures
localized in a finite depth interior to the water column. From an ecological
point of view, DCMs are evocative of a balance between the inflow of light from
the water surface and of nutrients from the sediment. From a (linear)
bifurcational point of view, they appear through a transcritical bifurcation in
which the trivial, no-plankton steady state is destabilized. This article is
devoted to the analytic investigation of the weakly nonlinear dynamics of these
DCM patterns, and it has two overarching themes. The first of these concerns
the fate of the destabilizing stationary DCM mode beyond the center manifold
regime. Exploiting the natural singularly perturbed nature of the model, we
derive an explicit reduced model of asymptotically high dimension which fully
captures these dynamics. Our subsequent and fully detailed study of this model
- which involves a subtle asymptotic analysis necessarily transgressing the
boundaries of a local center manifold reduction - establishes that a stable DCM
pattern indeed appears from a transcritical bifurcation. However, we also
deduce that asymptotically close to the original destabilization, the DCM
looses its stability in a secondary bifurcation of Hopf type. This is in
agreement with indications from numerical simulations available in the
literature. Employing the same methods, we also identify a much larger DCM
pattern. The development of the method underpinning this work - which, we
expect, shall prove useful for a larger class of models - forms the second
theme of this article.
