On Ebenman's model for the dynamics of a population with competing juveniles and adults

J. M. Cushing, Jia Li

Research output: Contribution to journalArticlepeer-review

39 Scopus citations


A general version of a model of Ebenman for the dynamics of a population consisting of competing juveniles and adults is analyzed using methods of bifurcation theory. A very general existence results is obtained for non-trivial equilibria and non-negative synchronous two-cycles that bifurcate simultaneously at the critical value r=1 of the inherent net reproductive rate r. Stability is studied in this general setting near the bifurcation point and conditions are derived that determine which of these two bifurcating branches is the stable branch. These general results are supplemented by numerical studies of the asymptotic dynamics over wider parameter ranges where various other bifurcations and stable attractors are found. The implications of these results are discussed with respect to the effects on stability that age class competition within a population can have and whether such competition is stabilizing or destabilizing.

Original languageEnglish (US)
Pages (from-to)687-713
Number of pages27
JournalBulletin of Mathematical Biology
Issue number6
StatePublished - Nov 1989
Externally publishedYes

ASJC Scopus subject areas

  • General Neuroscience
  • Immunology
  • General Mathematics
  • General Biochemistry, Genetics and Molecular Biology
  • General Environmental Science
  • Pharmacology
  • General Agricultural and Biological Sciences
  • Computational Theory and Mathematics


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