Equilibria in systems of interacting structured populations
type: Item
instance of: scholarly article
title: Equilibria in systems of interacting structured populations
zbMATH Open document ID: 0635.92014
DOI: 10.1007/BF00275507
published in: Journal of Mathematical Biology
publication date: 1987-01-01T00:00:00Z
review text: The existence of a stable positive equilibrium density for a community of k interacting structured species is studied as a bifurcation problem. Under the assumption that a subcommunity of k-1 species has a positive equilibrium and under only very mild restrictions on the density dependent vital growth rates, it is shown that a global continuum of equilibria for the full community bifurcates from the subcommunity equilibrium at a unique critical value of a certain inherent birth modulus for the k th species. Local stability is shown to depend upon the direction of the bifurcation. The direction of bifurcation is studied in more detail for the case when vital per unit birth and death rates depend upon population density through positive linear functionals of density and for the important case of two interacting species.
Mathematics Subject Classification ID: 92D25
Mathematics Subject Classification ID: 35B32
zbMATH DE Number: 4035631
zbMATH Keywords: communities of structured populations
zbMATH Keywords: competition
zbMATH Keywords: predator-prey interactions
zbMATH Keywords: existence of a stable positive equilibrium density
zbMATH Keywords: interacting structured species
zbMATH Keywords: subcommunity equilibrium
zbMATH Keywords: Local stability
zbMATH Keywords: direction of bifurcation
zbMATH Keywords: interacting species
author: J. M. Cushing
MaRDI profile type: Publication
Wikidata QID: Q68995322
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full work available at URL: https://doi.org/10.1007/bf00275507
OpenAlex ID: W1978982295
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description: scientific article; zbMATH DE number 4035631