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arXiv · 1710.02897

Spatial Dynamics of a Nonlocal Dispersal Population Model in a Shifting Environment

Wan-Tong Li·Jia-Bing Wang·Xiao-Qiang Zhao
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Abstract

This paper is concerned with spatial spreading dynamics of a nonlocal dispersal population model in a shifting environment where the favorable region is shrinking. It is shown that the species will become extinct in the habitat once the speed of the shifting habitat edge $c>c^*(\infty)$, however if $c<c^*(\infty)$, the species will persist and spread along the shifting habitat at an asymptotic spreading speed $c^*(\infty)$, where $c^*(\infty)$ is determined by the nonlocal dispersal kernel, diffusion rate and the maximum linearized growth rate. Moreover, we demonstrate that for any given speed of the shifting habitat edge, this model admits a nondecreasing traveling wave with the wave speed at which the habitat is shifting, which indicates that the extinction wave phenomenon does happen in such a shifting environment.

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Wan-Tong Li, Jia-Bing Wang, Xiao-Qiang Zhao. 2017-10-08. Spatial Dynamics of a Nonlocal Dispersal Population Model in a Shifting Environment. https://doi.org/10.1007/s00332-018-9445-2

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