Stability analysis and pattern selection of a plankton system with nonlocal predation

Abstract

A plankton micro-ecosystem composed of phytoplankton (prey) and zooplankton (predators with nonlocal predation) is researched. First, the Hopf bifurcation, the Turing bifurcation, and the strong/weak Turing-Hopf (TH) instability are gained with the help of linear stability analysis. Then, by the weakly nonlinear analysis, the amplitude equations for the pattern selection are calculated and show some types of patterns: spot patterns, stripe patterns and mixed patterns of the two. At last, the numerical simulations not only verify the analysis but also show the effect of the hunter function on the pattern selection. The results show that if the zooplankton hunt more dispersedly or diffuses faster, the plankton would gather and form denser patches. Besides, our analysis extends the application of the weakly nonlinear analysis and applies it to the nonlocal reaction-diffusion models.