Stability analysis of the plankton community with advection. (May 2021) - Liu, Zhi-bin; Liu, Shu-tang; Tian, Da-dong; Wang, Da
Highlights: When the advection velocities of all plankton are the same, the plankton community remains relatively stationary, and the advection at the same speed will not change the stability of the system but transfer the algae ecosystem as a whole. When the system is Hopf stable and Turing stable, if the advection velocities of phytoplankton and zooplankton are different, there is a wave bifurcation, the smallest convection speed difference that drives the system Wave unstable. When the system is Hopf stable but Turing unstable, We assign an advection speed zero and the other nonzero, there is a traveling bifurcation, the smallest convection speed difference that results in Traveling patterns. Abstract: We studied a spatial plankton community, comprising phytoplankton (prey) and zooplankton (predators), with advection. If the advection velocities of all plankton are the same, the plankton community remains relatively stationary. If the convection velocities are different, the speed difference will make the system unstable. When the original system without advection is Turing stable, due to the advection speed difference, there should be a Wave bifurcation, which will drive the system with advection Wave instability. If the original system without convection becomes Turing unstable, the system with advection will always be of Wave instability. Numerical simulations validated our analysis of stabilaity and showed more phenomena. When the original system without advection is Turing unstable, we keep the coefficient of one advection term zero and the other nonzero, the advection speed difference will produce traveling patterns (patterns on the traveling waves). If the speed difference is small enough, the patterns remain stationary, and if the speed difference increases, the traveling patterns appear. Therefore, there should be a Traveling bifurcation that separates stationary patterns and the traveling ones. The analysis and simulation experiments enrich the dynamics in the plankton models and contribute to a better understanding of the planktonic ecosystem in the real environment.