TURING INSTABILITY AND TRAVELING WAVES IN DIFFUSIVE PLANKTON MODELS WITH DELAYED NUTRIENT RECYCLING

In this paper we propose a reaction-diffusion system with two distribu ted delays to stimulate the growth of plankton communities in the lake s/oceans in which the plankton feeds on a limiting nutrient supplied a t a constant rate. The limiting nutrient is partially recycled after t he death of the organisms and a distributed delay is used to model nut rient recycling. The second delay is involved in the growth response o f the plankton to nutrient uptake. We first show that there are oscill ations (Hopf bifurcations) in the delay model induced by the second de lay. Then we study Turing (diffusion-driven) instability of the reacti on-diffusion system with delay. Finally, it is shown that if the delay model has a stable periodic solution, then the corresponding reaction -diffusion model with delay has a family of travelling waves.