Equilibria in systems of interacting structured populations

J. M. Cushing

Research output: Contribution to journalArticlepeer-review

10 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)627-649
Number of pages23
JournalJournal of mathematical biology
Issue number6
StatePublished - Feb 1987


  • Bifurcation
  • Communities of structured populations
  • Competition
  • Equilibria
  • Interacting species
  • Predator-prey inter-actions
  • Stability

ASJC Scopus subject areas

  • Modeling and Simulation
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics


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