Population growth and competition models with decay and competition consistent delay.
Chain transitive sets
Discrete delay differential equations
Extinction threshold
Local and global dynamics
Logistic growth
Lotka–Volterra competition
Journal
Journal of mathematical biology
ISSN: 1432-1416
Titre abrégé: J Math Biol
Pays: Germany
ID NLM: 7502105
Informations de publication
Date de publication:
19 04 2022
19 04 2022
Historique:
received:
30
06
2021
accepted:
26
03
2022
revised:
25
02
2022
entrez:
19
4
2022
pubmed:
20
4
2022
medline:
22
4
2022
Statut:
epublish
Résumé
We derive an alternative expression for a delayed logistic equation in which the rate of change in the population involves a growth rate that depends on the population density during an earlier time period. In our formulation, the delay in the growth term is consistent with the rate of instantaneous decline in the population given by the model. Our formulation is a modification of Arino et al. (J Theor Biol 241(1):109-119, 2006) by taking the intraspecific competition between the adults and juveniles into account. We provide a complete global analysis showing that no sustained oscillations are possible. A threshold giving the interface between extinction and survival is determined in terms of the parameters in the model. The theory of chain transitive sets and the comparison theorem for cooperative delay differential equations are used to determine the global dynamics of the model. We extend our delayed logistic equation to a system modeling the competition between two species. For the competition model, we provide results on local stability, bifurcation diagrams, and adaptive dynamics. Assuming that the species with shorter delay produces fewer offspring at a time than the species with longer delay, we show that there is a critical value, [Formula: see text], such that the evolutionary trend is for the delay to approach [Formula: see text].
Identifiants
pubmed: 35438310
doi: 10.1007/s00285-022-01741-3
pii: 10.1007/s00285-022-01741-3
doi:
Types de publication
Journal Article
Research Support, Non-U.S. Gov't
Langues
eng
Sous-ensembles de citation
IM
Pagination
39Informations de copyright
© 2022. The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
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