Biological invasion in a predator–prey model with a free boundary

Boundary Value Problems

Mohammad El Smaily¹  Lin Wang¹  Yunfeng Liu²  Zhiming Guo² 

[1] Department of Mathematics & Statistics, University of New Brunswick;School of Mathematics and Information Sciences, Guangzhou University;

关键词: Free boundary;    Biological invasions;    Predator–prey;    Spreading–vanishing dichotomy;   

DOI  :  10.1186/s13661-019-1147-7

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown