The minimal invasion speed of two competing species in homogeneous environment

Biological invasion has become an important element of global changes. In this paper, we use a reaction-diffusion system to discuss the minimal invasion speed of two competing species in the homogeneous environment. The general condition for the minimum invasion speed is obtained by applying the theory of propagation dynamics. Then the explicit conditions are derived by constructing upper solutions. The analytical results are corroborated by simulations of the considered reaction-diffusion system. Our results reveal the impact of the diffusion rate, growth rate, competitiveness of the species, as well as the carrying capacity of the environment, on the invasion speed, which provides an effective method for preventing biological invasion and controlling existing biological invasion.