Analysis and numerical simulation of phytoplankton-nutrient systems with nutrient loss

The dynamics of a mathematical model of a layer of single phytoplankton species growing over a pool of nutrients, proposed by [A.H. Taylor, J.R.W. Harris, J. Aiken, The interaction of physical and biological process in a model of the vertical distribution of phytoplankton under stratification, Mar. Int. Ecohyrd., J.C. Nihoul (Ed.) 42 (1986) 313-330] is analyzed. Both cases of presence and absence of a phytoplankton in the water below the layer of interest are considered. Positive and elementary stable nonstandard (PESN) methods, having the same qualitative features as the corresponding continuous models, are formulated and analyzed. Biological implications and a set of numerical simulations supporting the mathematical and numerical analysis are also presented.