A nonlocal population model for the invasion of Canada goldenrod

Jian Fang; Na Li; Chenhe Xu; Jian Fang; Na Li; Chenhe Xu

doi:10.3934/mbe.2022462

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 10: 9915-9937. doi: 10.3934/mbe.2022462

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A nonlocal population model for the invasion of Canada goldenrod

Jian Fang ^{1
,
,},
Na Li ¹,
Chenhe Xu ²

1.
School of Mathematics, Harbin Institute of Technology, Harbin, Heilongjiang 150001, China
2.
Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Kowloon Hong Kong, China

^*In memory of Professor Stephen A. Gourley.
Academic Editor: Feng-Bin Wang

Received: 09 November 2021 Revised: 26 June 2022 Accepted: 05 July 2022 Published: 12 July 2022

A mathematical model for the population invasion of Canada goldenrod is proposed, with two reproductive modes, yearly periodic time delay and spatially nonlocal response caused by the influence of wind on the seeds. Under suitable conditions, we obtain the existence of the rightward and leftward invasion speeds and their coincidence with the minimal speeds of time periodic traveling waves. Furthermore, the invasion speeds are finite if the dispersal kernel of seeds is exponentially bounded and infinite if dispersal kernel is exponentially unbounded.
- Canada goldenrod,
- periodic delay,
- nonlocal dispersal,
- propagation dynamics
Citation: Jian Fang, Na Li, Chenhe Xu. A nonlocal population model for the invasion of Canada goldenrod[J]. Mathematical Biosciences and Engineering, 2022, 19(10): 9915-9937. doi: 10.3934/mbe.2022462

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Abstract

A mathematical model for the population invasion of Canada goldenrod is proposed, with two reproductive modes, yearly periodic time delay and spatially nonlocal response caused by the influence of wind on the seeds. Under suitable conditions, we obtain the existence of the rightward and leftward invasion speeds and their coincidence with the minimal speeds of time periodic traveling waves. Furthermore, the invasion speeds are finite if the dispersal kernel of seeds is exponentially bounded and infinite if dispersal kernel is exponentially unbounded.

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