<p>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.</p>

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Propagation of Single-Species Models with Resource-Dependent Dispersal and Free Boundaries

  • Dawei Zhang,
  • Yun Huang,
  • Chufen Wu

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.