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Can a barrier zone stop invasion of a population?
Journal of Mathematical Biology ( IF 1.9 ) Pub Date : 2020-10-02 , DOI: 10.1007/s00285-020-01541-7
Bingtuan Li 1 , Minghua Zhang 1 , Bradley Coffman 1
Affiliation  

We consider an integro-difference model to study the effect of a stationary barrier zone on invasion of a population with a strong Allee effect. It is assumed that inside the barrier zone a certain proportion of the population is killed. A Laplace dispersal kernel is used in the model. We provide a formula for the critical width \(L^*\) of barrier zone. We show that when a barrier zone is set at the front of a population, if the width of barrier zone is bigger than \(L^*\) then the barrier zone can stop the population invasion, and if the width of barrier zone is less than \(L^*\) then the population crosses the barrier zone and eventually occupies the entire space. The results are proven by establishing the existence and attractivity of three types of equilibrium solutions. The mathematical proofs involve phase plane analysis and comparison.



中文翻译:

屏障区可以阻止人口的入侵吗?

我们考虑使用积分差分模型来研究静止屏障区对具有强 Allee 效应的种群入侵的影响。假设在屏障区域内,一定比例的人口被杀死。模型中使用了拉普拉斯扩散核。我们提供了障碍区临界宽度\(L^*\)的公式。我们证明,当在种群的前面设置障碍区时,如果障碍区的宽度大于\(L^*\),那么障碍区可以阻止种群的入侵,如果障碍区的宽度为小于\(L^*\)然后人口越过障碍区并最终占据整个空间。通过建立三种平衡解的存在性和吸引力来证明结果。数学证明涉及相平面分析和比较。

更新日期:2020-10-02
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