Persistence versus extinction for a class of discrete-time structured population models.
J Math Biol
; 72(4): 821-850, 2016 Mar.
Article
em En
| MEDLINE
| ID: mdl-26032653
ABSTRACT
We provide sharp conditions distinguishing persistence and extinction for a class of discrete-time dynamical systems on the positive cone of an ordered Banach space generated by a map which is the sum of a positive linear contraction A and a nonlinear perturbation G that is compact and differentiable at zero in the direction of the cone. Such maps arise as year-to-year projections of population age, stage, or size-structure distributions in population biology where typically A has to do with survival and individual development and G captures the effects of reproduction. The threshold distinguishing persistence and extinction is the principal eigenvalue of (II−A)(−1)G'(0) provided by the Krein-Rutman Theorem, and persistence is described in terms of associated eigenfunctionals. Our results significantly extend earlier persistence results of the last two authors which required more restrictive conditions on G. They are illustrated by application of the results to a plant model with a seed bank.
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Texto completo:
1
Coleções:
01-internacional
Base de dados:
MEDLINE
Assunto principal:
Extinção Biológica
/
Modelos Biológicos
Tipo de estudo:
Prognostic_studies
Limite:
Animals
Idioma:
En
Revista:
J Math Biol
Ano de publicação:
2016
Tipo de documento:
Article
País de afiliação:
Estados Unidos