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Title: Intra-specific competition and insect larval development : a model with time-dependent delay
Authors: Gourley, SA
Liu, R
Lou, Y 
Issue Date: Apr-2017
Source: Proceedings of the Royal Society of Edinburgh. Section A : mathematics, Apr. 2017, v. 147, no. 2, p. 353-369
Abstract: We derive a stage-structured model for an insect population in which a larva matures on reaching a certain size, and in which there is intra-specific competition among larvae that hinders their development, thereby prolonging the larval phase. The model, a system of delay differential equations for the total numbers of adults and larvae, assumes two forms. One of these is a system with a variable state-dependent time delay determined by a threshold condition, the other has constant and distributed delays, a size-like independent variable replacing time t, and no threshold condition. We prove theorems on boundedness and on the linear stability of equilibria.
Keywords: Competition
Delay
Size-structure
Stability
Boundedness
Publisher: Cambridge University Press
Journal: Proceedings of the Royal Society of Edinburgh. Section A : mathematics 
ISSN: 0308-2105
EISSN: 1473-7124
DOI: 10.1017/S0308210516000159
Rights: This article has been published in a revised form in Proceedings of the Royal Society of Edinburgh Section A: Mathematics http://doi.org/10.1017/S0308210516000159. This version is free to view and download for private research and study only. Not for re-distribution or re-use. © 2017 The Royal Society of Edinburgh.
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 Proceedings of the Royal Society of Edinburgh Section A: Mathematics https://dx.doi.org/10.1017/S0308210516000159.
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