Bifurcation of periodic oscillations due to delays in single species growth models

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3 Scopus citations

Abstract

Theorems are given which guarantee the bifurcation of non-constant, periodic solutions (of fixed period) of a scalar functional equation with two independent parameters. These results are applied to a single, isolated species growth model of general form with a general Volterra (Stieltjes) delay using the 'magnitudes' of the instantaneous and delayed growth rate responses as the independent bifurcation parameters. The case of linear growth rate responses (i.e. delay logistic models) is considered in more detail, particularly the often studied single lag logistic equation.

Original languageEnglish (US)
Pages (from-to)145-161
Number of pages17
JournalJournal of mathematical biology
Volume6
Issue number2
DOIs
StatePublished - Jul 1 1978

Keywords

  • Delays
  • Growth models
  • Oscillations

ASJC Scopus subject areas

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

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