| Summary: | Abstract In this paper we study a predator–prey system with free boundary in a one-dimensional environment. The predator v is the invader which exists initially in a sub-interval [0,s0] $[0, s_{0}]$ of [0,L] $[0,L]$ and has the Leslie–Gower terms that measure the loss in the predator population due to rarity of the prey. The prey u (the native species) is initially distributed over the whole region [0,L] $[0,L]$. Our primary goal is to understand how the success or failure of the predator’s invasion is affected by the initial datum v0 $v_{0}$. We derive a spreading–vanishing dichotomy and give sharp criteria for spreading and vanishing in this model.
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