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Asymptotic propagations of a nonlocal dispersal population model with shifting habitats

Part of: Parabolic equations and systems Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  16 June 2021

SHAO-XIA QIAO ,
WAN-TONG LI  and
JIA-BING WANG
SHAO-XIA QIAO
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, P.R. China emails: qiaoshx14@lzu.edu.cn; wtli@lzu.edu.cn
WAN-TONG LI
Affiliation:
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, P.R. China emails: qiaoshx14@lzu.edu.cn; wtli@lzu.edu.cn
JIA-BING WANG
Affiliation:
School of Mathematics and Physics, Center for Mathematical Sciences, China University of Geosciences, Wuhan 430074, P.R. China email: wangjb@cug.edu.cn
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Abstract

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This paper is concerned with the asymptotic propagations for a nonlocal dispersal population model with shifting habitats. In particular, we verify that the invading speed of the species is determined by the speed c of the shifting habitat edge and the behaviours near infinity of the species’ growth rate which is nondecreasing along the positive spatial direction. In the case where the species declines near the negative infinity, we conclude that extinction occurs if c > c*(∞), while c < c*(∞), spreading happens with a leftward speed min{−c, c*(∞)} and a rightward speed c*(∞), where c*(∞) is the minimum KPP travelling wave speed associated with the species’ growth rate at the positive infinity. The same scenario will play out for the case where the species’ growth rate is zero at negative infinity. In the case where the species still grows near negative infinity, we show that the species always survives ‘by moving’ with the rightward spreading speed being either c*(∞) or c*(−∞) and the leftward spreading speed being one of c*(∞), c*(−∞) and −c, where c*(−∞) is the minimum KPP travelling wave speed corresponding to the growth rate at the negative infinity. Finally, we give some numeric simulations and discussions to present and explain the theoretical results. Our results indicate that there may exists a solution like a two-layer wave with the propagation speeds analytically determined for such type of nonlocal dispersal equations.

Keywords

Nonlocal dispersal modelasymptotic propagationshifting habitat

MSC classification

Primary: 35K57: Reaction-diffusion equations 35R20: Partial operator-differential equations (i.e., PDE on finite-dimensional spaces for abstract space valued functions)
Secondary: 92D25: Population dynamics (general)
Type
Papers
Information
European Journal of Applied Mathematics , Volume 33 , Issue 4 , August 2022 , pp. 701 - 728
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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