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Can a barrier zone stop invasion of a population?

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, University of Louisville, Louisville, KY, 40292, USA

    Bingtuan Li, Minghua Zhang & Bradley Coffman

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  1. Bingtuan Li
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  2. Minghua Zhang
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  3. Bradley Coffman
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Correspondence to Bingtuan Li.

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B. Li and M. Zhang were partially supported by the National Science Foundation under Grant DMS-1515875, and B. Li and B. Coffman were partially supported by the National Science Foundation under Grant DMS-1951482.

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Li, B., Zhang, M. & Coffman, B. Can a barrier zone stop invasion of a population?. J. Math. Biol. 81, 1193–1216 (2020). https://doi.org/10.1007/s00285-020-01541-7

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  • DOI: https://doi.org/10.1007/s00285-020-01541-7

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