The Effect of Advection

A spatial plankton community which comprises phytoplankton (prey) and zooplankton (predators) with advection has been studied. It is well known that when the advection velocities of all plankton remain the same, the plankton community is relatively stationary. And the speed difference will make the system unstable because that the convection velocities become different. As the original system without advection becomes Turing stable, there should exist a wave bifurcation due to the advection speed difference, driving the system with advection wave instability. As the original system without convection remains Turing unstable, there will always exist wave instability for the system with advection. Numerical simulations not only validated our analysis of stability but also showed more phenomena. If the original system without advection remains Turing unstable, and when we take the coefficient of one advection term as zero and the other as nonzero, there will emerge traveling patterns (patterns on the traveling waves) produced by advection speed difference. When the speed difference becomes small enough, the patterns become stationary. And as the speed difference increases, there appear the traveling patterns. Thus, a traveling bifurcation should be generated which separates stationary patterns and the traveling ones. The results about analysis and simulations enrich the dynamics study of the plankton models and have contribution for a better understanding of the planktonic ecosystem in the real environment.