Dynamics of a marine plankton system: Diffusive instability and pattern formation

The paper deals with the study of the stability behavior of a marine prey–predator (phytoplankton–zooplankton) system. The interaction of the phytoplankton with zooplankton is taken as the Ivlev type functional response. The stability behaviors of the reaction–diffusion system arising from the zooplankton–phytoplankton model are carried out. We have studied the reaction–diffusion equation with both constant and variable (periodic) diffusion coefficients. For constant diffusion we have analyzed the effect of diffusion for diffusive instability of the system. The temporal variation of the system with small periodicity of diffusive coefficient have been studied by using Hill’s equation. We have carried out the numerical simulation to support and supplement the analytical results.