A free boundary problem for the diffusive intraguild predation model with intraspecific competition

Abstract

In this paper, we investigate a free boundary problem for the diffusive intraguild predation model with intraspecific competition in one dimensional space. The main objective is to portray the asymptotic behavior of spread of an invasive or new predator species via a free boundary. In this model, we assume both the IG prey and the IG (invasive/new) predator species with intraspecific competition, and the IG predator species can only expand further into the new environment from the right end of the initial region. In both cases, we prove a spreading–vanishing dichotomy for this model, specifically, the IG predator species either successfully spreads to infinity as t → ∞ at the front and survives in the new environment, or spreads within a bounded area and dies out in the long run. The long time behavior of ( R , N , P ) and criteria for spreading and vanishing are also obtained.