Propagation of Single-Species Models with Resource-Dependent Dispersal and Free Boundaries
摘要
This paper is concerned with the propagation of single-species models with resource-dependent dispersal and free boundaries. For long time behaviors of global solutions, a spreading-vanishing dichotomy is established. Moreover, we obtain sharp criteria on spreading and vanishing by investigating the associated linearized eigenvalue problem. The theoretical analyses indicate that: (1) The small dispersal rate increasing the possibility of successful spread; (2) Otherwise, the success or failure in spreading depends on the coefficient in free boundaries condition. Since the principal eigenvalue depends on both dispersal and resource, our results reveal that resource-dependent dispersal is more beneficial to the survival of species compared with random dispersal.