Mathematical Study of a Resource-Based Diffusion Model with Gilpin-Ayala Growth and Harvesting.
Directed diffusion
Gilpin–Ayala
Global attraction
Harvesting
Journal
Bulletin of mathematical biology
ISSN: 1522-9602
Titre abrégé: Bull Math Biol
Pays: United States
ID NLM: 0401404
Informations de publication
Date de publication:
15 09 2022
15 09 2022
Historique:
received:
11
01
2022
accepted:
29
08
2022
entrez:
15
9
2022
pubmed:
16
9
2022
medline:
20
9
2022
Statut:
epublish
Résumé
This paper focuses on a Gilpin-Ayala growth model with spatial diffusion and Neumann boundary condition to study single species population distribution. In our heterogeneous model, we assume that the diffusive spread of population is proportional to the gradient of population per unit resource, rather than the population density itself. We investigate global well-posedness of the mathematical model, determine conditions on harvesting rate for which non-trivial equilibrium states exist and examine their global stability. We also determine conditions on harvesting that leads to species extinction through global stability of the trivial solution. Additionally, for time periodic growth, resource, capacity and harvesting functions, we prove existence of time-periodic states with the same period. We also present numerical results on the nature of nonzero equilibrium states and their dependence on resource and capacity functions as well as on Gilpin-Ayala parameter [Formula: see text]. We conclude enhanced effects of diffusion for small [Formula: see text] which in particular disallows existence of nontrivial states even in some cases when intrinsic growth rate exceeds harvesting at some locations in space for which a logistic model allows for a nonzero equilibrium density.
Identifiants
pubmed: 36107169
doi: 10.1007/s11538-022-01074-8
pii: 10.1007/s11538-022-01074-8
doi:
Types de publication
Journal Article
Research Support, N.I.H., Extramural
Langues
eng
Sous-ensembles de citation
IM
Pagination
120Subventions
Organisme : NIGMS NIH HHS
ID : R01 GM118553
Pays : United States
Organisme : NIAID NIH HHS
ID : R01 AI158963
Pays : United States
Informations de copyright
© 2022. The Author(s), under exclusive licence to Society for Mathematical Biology.
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