Model of the nitrogen transformation cycle

The purpose of this paper is to investigate a system of parabolic equations with discrete time delays describing a nitrogen transformation cycle in an aquatic environment, which consists of the four kinds of living organisms (phytoplankton and microorganisms), and four cases of dissolved organic and inorganic nutrients and detritus. When the delays are relatively small, our predictions are identical to the predictions given by the corresponding PDE. The system of parabolic equations is discretized by the finite difference method which yields a coupled system of nonlinear algebraic equations. Stability analysis of equilibria and some numerical examples are given. It is shown that Hopf bifurcation may occur.