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

Y Kyrychko, SA Gourley, MV Bartuccelli

Research output: Contribution to journalArticle (Academic Journal)peer-review

20 Citations (Scopus)

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.
Translated title of the contributionDynamics of a stage-structured population model on an isolated lattice
Original languageEnglish
Pages (from-to)1688 - 1708
Number of pages21
JournalSIAM Journal on Mathematical Analysis
Volume37 (5)
DOIs
Publication statusPublished - Jan 2006

Bibliographical note

Publisher: SIAM Publications

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