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 contribution | Dynamics of a stage-structured population model on an isolated lattice |
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Original language | English |
Pages (from-to) | 1688 - 1708 |
Number of pages | 21 |
Journal | SIAM Journal on Mathematical Analysis |
Volume | 37 (5) |
DOIs | |
Publication status | Published - Jan 2006 |