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|
|Pages (from-to)||1688 - 1708|
|Number of pages||21|
|Journal||SIAM Journal on Mathematical Analysis|
|Publication status||Published - Jan 2006|