Invasion by an inferior or superior competitor: A diffusive competition model with a free boundary in a heterogeneous environment

In this study, we consider the population dynamics of an invasive species and a resident species, which are modeled as a diffusive competition process in a radially symmetric setting with a free boundary. We assume that the resident species undergoes diffusion and growth in RnRn, while the invasive species initially exists in a finite ball, but invades the environment with a spreading front evolving according to a free boundary. When the invasive species is inferior, we show that if the resident species is already well established initially, then the invader can never invade deep into the underlying habitat, thus it dies out before its invading front reaches a certain finite limiting position. When the invasive species is superior, a spreading–vanishing dichotomy holds, and sharp criteria for spreading and vanishing with d1d1, μ  , and u0u0 as variable factors are obtained, where d1d1, μ  , and u0u0 are the dispersal rate, expansion capacity, and initial number of invaders, respectively. In particular, we obtain some rough estimates of the asymptotic spreading speed when spreading occurs.