@article{68da980ad9424942a93ac80cd3d862d9,
title = "A Delayed Succession Model with Diffusion for the Impact of Diapause on Population Growth",
abstract = "Diapause, a period of arrested development driven by adverse environmental conditions, plays an important role in the establishment and invasion of insects and other invertebrate organisms in temperate and subtropical areas. In order to describe the spatial dynamics of diapausing species, we propose a novel model involving (a) seasonal succession to distinguish the normal growth period, diapause period, and postdiapause period; (b) a diffusion term to represent the random movement of species; and (c) a maturation delay term to describe the developmental duration of species. We first study the model in a bounded domain for the survival and establishment of a species. The extinction and persistence of the species can be predicted by the basic reproduction ratio \textbackslash{}scrR 0. Then we investigate the model in an unbounded domain for the spreading of the species. Our results show that the minimal wave speed for a periodic traveling wave is equal to the spreading speed. Numerical simulations are performed to validate theoretical results and in particular to compare the effects of two diapausing strategies: diapausing in the adult stage and in the immature stage.",
keywords = "Basic reproduction ratio, Diapause, Spreading speed, Traveling waves",
author = "Zhenguo Bai and Yijun Lou and Zhao, \{Xiao Qiang\}",
note = "Funding Information: \textbackslash{}ast Received by the editors January 2, 2019; accepted for publication (in revised form) March 27, 2020; published electronically June 16, 2020. https://doi.org/10.1137/19M1236448 Funding: The work of the first author was supported by the NSF of China through grants 11971369 and 11671315, by the NSF of Shaanxi Province of China through grant 2019JM-241, and by the Fundamental Research Funds for the Central Universities through grant JB190705. The work of the second author was supported by the Research Grants Council of Hong Kong. The work of the third author was supported by the NSERC. \textbackslash{}dagger School of Mathematics and Statistics, Xidian University, Xi'an 710071, People's Republic of China (
[email protected]). \textbackslash{}ddagger Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong (
[email protected]). \textbackslash{}S Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C 5S7, Canada (
[email protected]). Publisher Copyright: \textbackslash{}bigcirc c 2020 Society for Industrial and Applied Mathematics Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = jun,
doi = "10.1137/19M1236448",
language = "English",
volume = "80",
pages = "1493--1519",
journal = "SIAM Journal on Applied Mathematics",
issn = "0036-1399",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",
}