Dynamical behavior of a reaction-diffusion-advection chemostat model with Holling III function

This paper deals with a reaction-diffusion-advection chemostat model with Holling III function. By regarding growth rates of two species as variable parameters, we mainly study the effects of growth rates on extinction and survival of species. More precisely, there exist two critical growth rates and two critical curves, which classify the dynamics of the system into three scenarios: (1) extinction; (2) competitive exclusion; (3) coexistence. As a further development, we take numerical approaches to study the effect of diffusion rates and advection rates on system dynamics and the geometric structure of two critical curves. These interesting analytical and numerical results are instructive and may have important biological implications on this kind of reaction-diffusion-advection chemostat models.