Spatialtemporal Dynamics Of A Diffusive Mussel-algae System

We investigate a reaction–diffusion–advection system which characterizes the interactions between the algae and mussels in advective environments,such as streams or rivers.In contrast with non-advective environments,the dynamics of this system is more complicated.By analyzing the semi-trivial steady state and its corresponding eigenvalue problem,we get the global dynamical behaviors.It turns out that there exists one critical advection rate and one critical di?usion rate of algae,which classify the dynamic behavior of this system into two scenarios,that is,(i)the mussels become extinct and the algae survives in the long run;(ii)the mussels will coexist permanently with the algae.By means of numerical simulations,the e?ects of di?usion and advection on the dynamics of this system are investigated.