Global dynamics of a competition model with nonlocal dispersal II: The full system

In this paper, we study logistic models with non-local dispersal for two competing species. In the weak competition case, the global asymptotic behavior of solutions is completely classified provided one of the following conditions is valid:
• one diffusion rate is small;
• one diffusion rate is large;
• two diffusion rates are close. This is a continuation of the work [16]. Our results illustrate the effects of non-local dispersals and interspecific competition coefficients in the competition system with spatially heterogeneous environments.