A Leslie-Gower predator-prey model with a free boundary

TL;DR

This paper analyzes a Leslie-Gower predator-prey model with a free boundary in a one-dimensional environment, establishing conditions for species spreading or vanishing and determining spreading speeds.

Contribution

It provides new criteria for spreading success or failure and characterizes the spreading speed in a free boundary predator-prey model.

Findings

Conditions for spreading success and failure

Sharp criteria for species vanishing or spreading

Spreading speed bounds between wavefront and elliptic solutions

Abstract

In this paper, we consider a Leslie-Gower predator-prey model in one-dimensional environment. We study the asymptotic behavior of two species evolving in a domain with a free boundary. Sufficient conditions for spreading success and spreading failure are obtained. We also derive sharp criteria for spreading and vanishing of the two species. Finally, when spreading is successful, we show that the spreading speed is between the minimal speed of traveling wavefront solutions for the predator-prey model on the whole real line (without a free boundary) and an elliptic problem that follows from the original model.