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Title: Spatial dynamics of a nonlocal model with periodic delay and competition
Authors: Zhang, L
Liu, KH 
Lou, YJ 
Wang, ZC
Issue Date: Dec-2020
Source: European journal of applied mathematics, Dec. 2020, v. 31, no. 6, p. 1070-1100
Abstract: Each species is subject to various biotic and abiotic factors during growth. This paper formulates a deterministic model with the consideration of various factors regulating population growth such as age-dependent birth and death rates, spatial movements, seasonal variations, intra-specific competition and time-varying maturation simultaneously. The model takes the form of two coupled reaction–diffusion equations with time-dependent delays, which bring novel challenges to the theoretical analysis. Then, the model is analysed when competition among immatures is neglected, in which situation one equation for the adult population density is decoupled. The basic reproduction number is defined and shown to determine the global attractivity of either the zero equilibrium (when ) or a positive periodic solution ( ) by using the dynamical system approach on an appropriate phase space. When the immature intra-specific competition is included and the immature diffusion rate is neglected, the model is neither cooperative nor reducible to a single equation. In this case, the threshold dynamics about the population extinction and uniform persistence are established by using the newly defined basic reproduction number as a threshold index. Furthermore, numerical simulations are implemented on the population growth of two different species for two different cases to validate the analytic results.
Keywords: Age structure
Diffusion
Seasonal effects
Periodic delay
Intra-specific competition
Publisher: Cambridge University Press
Journal: European journal of applied mathematics
ISSN: 0956-7925
EISSN: 1469-4425
DOI: 10.1017/S0956792519000408
Rights: This article has been published in a revised form in European Journal of Applied Mathematics https://dx.doi.org/10.1017/S0956792519000408. This version is free to view and download for private research and study only. Not for re-distribution or re-use. © The Author(s) 2020. Published by Cambridge University Press.
When citing an Accepted Manuscript or an earlier version of an article, the Cambridge University Press requests that readers also cite the Version of Record with a DOI link. The article is subsequently published in revised form in European Journal of Applied Mathematics https://dx.doi.org/10.1017/S0956792519000408
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