Nontrivial Periodic Solutions of Marine Ecosystem Models of N-DOP type

Abstract

We investigate marine ecosystem models of N-DOP type with regard to nontrivial periodic solutions. The elements of this important, widely-used model class typically consist of two coupled advection-diffusion-reaction equations. The corresponding reaction terms are divided into a linear part, describing the transformation of one model variable into the other, and a bounded nonlinear part. Additionally, the model equations conserve the mass contained in the system, i.e. the masses of both variables add up to a constant total mass. In particular, the trivial function is a periodic solution. In this paper, we prove that there is at least one periodic solution for every prescribed total mass. The proof makes use of the typical properties of N-DOP type models by combining results from monotone operator theory and a fixed point argument. In the end, we apply the theorem to the PO4-DOP model, an N-DOP type model which is well-known and often used.