Global branches of equilibrium solutions of the McKendrick equations for age-structured population growth

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

The existence of positive equilibrium solutions of the McKendrick equations for the dynamics of an age-structured population is studied as a bifurcation phenomenon using the inherent net reproductive rate n as a bifurcation parameter. Under only continuity assumptions on the density dependent death and tertility rates, it is shown that a global continuum of positive equilibria exists in a certain Banach space. This continuum connects from the trivial solution at n = 1 to the boundary of the domain on which the problem is posed. Results concerning the spectrum are given. In particular, some circumstances are described under which positive equilibria exist for all n values greater than the critical value n = 1.

Original languageEnglish (US)
Pages (from-to)175-188
Number of pages14
JournalComputers and Mathematics with Applications
Volume11
Issue number1-3
DOIs
StatePublished - Jan 1 1985

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

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