Instability in diffusive ecological models with nonlocal delay effects

We propose a reaction-diffusion system with nonlocal delays to model the growth of plankton communities feeding on a limiting nutrient supplied at a constant rate. Two delays are incorporated into the model: one describes the delayed nutrient recycling process and the other models the delayed growth response of the plankton. It is assumed that both delays are nonlocal in the sense that there are delayed not only in time but also in space. Local and bifurcation analyses are carried out. It has been shown that Turing-type spatial patterns occur when the diffusion coefficients vary and temporal or spatial-temporal patterns occur when the delay involved in the growth response changes.