Document Detail


Equilibria in systems of interacting structured populations.
MedLine Citation:
PMID:  3572260     Owner:  NLM     Status:  MEDLINE    
Abstract/OtherAbstract:
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 kth species. Local stability is shown to depend upon the direction of bifurcation. The direction of bifurcation is studied in more detail for the case when vital per unity birth and death rates depend on population density through positive linear functionals of density and for the important case of two interacting species. Some examples involving competition, predation and epidemics are given.
Authors:
J M Cushing
Publication Detail:
Type:  Journal Article    
Journal Detail:
Title:  Journal of mathematical biology     Volume:  24     ISSN:  0303-6812     ISO Abbreviation:  J Math Biol     Publication Date:  1987  
Date Detail:
Created Date:  1987-05-27     Completed Date:  1987-05-27     Revised Date:  2004-11-17    
Medline Journal Info:
Nlm Unique ID:  7502105     Medline TA:  J Math Biol     Country:  GERMANY, WEST    
Other Details:
Languages:  eng     Pagination:  627-49     Citation Subset:  IM    
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MeSH Terms
Descriptor/Qualifier:
Animals
Biometry
Epidemiology
Humans
Models, Biological*
Population Density*
Population Dynamics*
Predatory Behavior

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