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Dynamics of a stage-structured population model on an isolated finite lattice

Kyrychko, Y, Gourley, SA and Bartuccelli, MV (2006) Dynamics of a stage-structured population model on an isolated finite lattice SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 37 (5). 1688 - 1708. ISSN 0036-1410

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Abstract

In this paper we derive a stage-structured model for a single species on a finite one-dimensional lattice. There is no migration into or from the lattice. The resulting system of equations, to be solved for the total adult population on each patch, is a system of delay equations involving the maturation delay for the species, and the delay term is nonlocal involving the population on all patches. We prove that the model has a positivity preserving property. The main theorems of the paper are comparison principles for the cases when the birth function is increasing and when the birth function is a nonmonotone function. Using these theorems we prove results on the global stability of a positive equilibrium.

Item Type: Article
Uncontrolled Keywords: Science & Technology, Physical Sciences, Mathematics, Applied, Mathematics, EQUATIONS
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Divisions: Faculty of Engineering and Physical Sciences > Mathematics
Depositing User: Mr Adam Field
Date Deposited: 27 May 2010 14:40
Last Modified: 23 Sep 2013 18:33
URI: http://epubs.surrey.ac.uk/id/eprint/1427

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