Dynamic behaviors of a reaction–diffusion competition system with road diffusion and nonlocal interaction

Abstract

We present a two-species competition system that incorporates road diffusion and non-local interactions, which describes a process of biological invasion. Using the modified comparison principle, we derive that the system possesses a unique global solution. We analyze the long-term behavior of the competing populations, that is, whether the invasion succeeds or fails. Our analysis reveals that in cases of weak–strong interaction between species, the weaker one tends to extinction, whereas the stronger one persists. In contrast, when the competition is characterized as weak-weak, both species are able to coexist simultaneously. Additionally, it is demonstrated that the invasion velocity exceeds the speed of traveling wave solutions when the road diffusion coefficient is sufficiently large.