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.
Highlights
A variety of models are used to describe the predator-prey interactions
We considered a Leslie-Gower and Holling-type II predator-prey model in a one-dimensional environment
(i) Theorem 4.2 and Theorem 4.3 provide the asymptotic behavior of the two species when spreading success and spreading failure, in terms of h∞: If h∞ = +∞, we have lim u(t, x) = u∗, lim υ(t, x) = υ∗
Summary
Mathematics Subject Classification (2010). Primary: 35K57, 35R35, 92C50, 92B99. Keywords. Free Boundary; Leslie-Gower; Biological Invasive, PredatorPrey; Spreading-Vanishing Dichotomy. Yunfeng Liu a,b, Zhiming Guo a,∗, Mohammad El Smaily b and Lin Wang b a School of Mathematics and Information Science, Guangzhou University Guangzhou, 510006, PR China b Department of Mathematics and Statistics, University of New Brunswick Fredericton, NB, Canada
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