Dynamics for a two-species competition-diffusion model with two free boundaries 1

Jong Shenq Guo*, Chang-Hong Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

70 Scopus citations

Abstract

To understand the spreading and interaction of two-competing species, we study the dynamics for a two-species competition-diffusion model with two free boundaries. Here, the two free boundaries which describe the spreading fronts of two competing species, respectively, may intersect each other. Our result shows there exists a critical value such that the superior competitor always spreads successfully if its territory size is above this constant at some time. Otherwise, the superior competitor can be wiped out by the inferior competitor. Moreover, if the inferior competitor does not spread fast enough such that the superior competitor can catch up with it, the inferior competitor will be wiped out eventually and then a spreading-vanishing trichotomy is established. We also provide some characterization of the spreading-vanishing trichotomy via some parameters of the model. On the other hand, when the superior competitor spreads successfully but with a sufficiently low speed, the inferior competitor can also spread successfully even the superior species is much stronger than the weaker one. It means that the inferior competitor can survive if the superior species cannot catch up with it.

Original languageEnglish
Article number1
Pages (from-to)1-27
Number of pages27
JournalNonlinearity
Volume28
Issue number1
DOIs
StatePublished - 1 Jan 2015

Keywords

  • Competition-diffusion model
  • Free boundary problem
  • Population dynamics
  • Spreading-vanishing trichotomy

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