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

摘要

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 R-n, 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 d(1), mu, and u(0) as variable factors are obtained, where d(1) mu, and u(0) 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. (C) 2014 Elsevier Inc. All rights reserved.