Dynamics induced by delay in a nutrient-phytoplankton model with diffusion

In this paper, a nutrient-phytoplankton model described by a couple of reaction-diffusion equations with delay is studied analytically and numerically. The aim of this research is to provide an understanding of the impact of delay on the nutrient-phytoplankton dynamics. Significantly, the delay can not only induce instability of a positive equilibrium, but also promote the formation of patchiness (an irregular pattern) via Hopf bifurcation. However, if the delay does not exist, the positive equilibrium is always globally asymptotically stable when it exists. In addition, the numerical analysis indicates that the input rate and the loss rate of nutrient also play an important role in the growth of phytoplankton, which supports that eutrophic conditions may be a significant reason inducing phytoplankton blooms. Numerical results are consistent with the analytical results.