A Bifurcation Analysis of Size Structured Phyto-Zooplankton Models
R.W. Scheffers (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Y.M. Dijkstra – Mentor (TU Delft - Electrical Engineering, Mathematics and Computer Science)
J.L.A. Dubbeldam – Mentor (TU Delft - Electrical Engineering, Mathematics and Computer Science)
S. Jain – Graduation committee member (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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Abstract
Modeling plankton communities has been an import topic in mathematical biology for quite some time. Previous research mostly comes in two flavors. On one hand we have large global models, which try and recreate measured data, but often lose track of what are the root causes of phenomena. On the other hand we have smaller models, where the (mathematical) reasoning behind phenomena are tried to be understood, but they lose some of their applicability. We try to bridge the gap between these two, by exploring how far results after simplification carry over to a more general case. We do this by investigating a size structured plankton model as proposed by (Poulin & Franks, 2010). We first simplify the interaction between phyto- and zooplankton, for which we are able to find analytical stationary solutions. Using numerical methods we are able to show stable stationary and limit cycle behavior. Furthermore we are able to show how much diversity remains, and how this is linked to the analytical solutions. Then we are able to show that these structures remain in place after allowing more complex interactions, and identify how far this remains true. Using this knowledge we are able to give quick insights into more complex models.