An alternative delayed population growth difference equation model.
Beverton–Holt model
Componentwise monotonicity
Delay difference equation
Delayed Beverton–Holt/Pielou model
Discretization
Extinction threshold
Global stability
Logistic growth
Single species growth models
Journal
Journal of mathematical biology
ISSN: 1432-1416
Titre abrégé: J Math Biol
Pays: Germany
ID NLM: 7502105
Informations de publication
Date de publication:
07 08 2021
07 08 2021
Historique:
received:
12
10
2020
accepted:
18
07
2021
revised:
13
05
2021
entrez:
7
8
2021
pubmed:
8
8
2021
medline:
21
10
2021
Statut:
epublish
Résumé
We propose an alternative delayed population growth difference equation model based on a modification of the Beverton-Holt recurrence, assuming a delay only in the growth contribution that takes into account that those individuals that die during the delay, do not contribute to growth. The model introduced differs from a delayed logistic difference equation, known as the delayed Pielou or delayed Beverton-Holt model, that was formulated as a discretization of the Hutchinson model. The analysis of our delayed difference equation model identifies a critical delay threshold. If the time delay exceeds this threshold, the model predicts that the population will go extinct for all non-negative initial conditions. If the delay is below this threshold, the population survives and its size converges to a positive globally asymptotically stable equilibrium that is decreasing in size as the delay increases. We show global asymptotic stability of the positive equilibrium using two different techniques. For one set of parameter values, a contraction mapping result is applied, while the proof for the remaining set of parameter values, relies on showing that the map is eventually componentwise monotone.
Identifiants
pubmed: 34363540
doi: 10.1007/s00285-021-01652-9
pii: 10.1007/s00285-021-01652-9
doi:
Types de publication
Journal Article
Research Support, Non-U.S. Gov't
Langues
eng
Sous-ensembles de citation
IM
Pagination
25Informations de copyright
© 2021. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
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