Abstract
This paper is concerned with the spatial dynamics of a nonlocal dispersal population model in a shifting environment where the favorable region is shrinking. It is shown that the species becomes extinct in the habitat if the speed of the shifting habitat edge \(c>c^*(\infty )\), while the species persists and spreads along the shifting habitat at an asymptotic speed \(c^*(\infty )\) if \(c<c^*(\infty )\), 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, the model system 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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Acknowledgements
Our sincere thanks goes to Dr. Jian Fang for his helpful discussion on the construction of the subsolution for the wave profile equation (4.3). We are also grateful to two anonymous referees for their careful reading and valuable suggestions which led to an improvement of our original manuscript. W.-T. Li was partially supported by NSF of China (11671180, 11731005) and FRFCU (lzujbky-2017-ct01). J.-B. Wang would like to thank the China Scholarship Council (201606180060) for financial support during the period of his overseas study and to express his gratitude to the Department of Mathematics and Statistics, Memorial University of Newfoundland, for its kind hospitality. X.-Q. Zhao was partially supported by the NSERC of Canada.
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Communicated by Philip K. Maini.
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Li, WT., Wang, JB. & Zhao, XQ. Spatial Dynamics of a Nonlocal Dispersal Population Model in a Shifting Environment. J Nonlinear Sci 28, 1189–1219 (2018). https://doi.org/10.1007/s00332-018-9445-2
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DOI: https://doi.org/10.1007/s00332-018-9445-2