Estimates of predator-prey limit cycles

Donald L. De Angelis

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

Perturbation methods are applied to a differential equation predator-prey model to find the approximate amplitudes and period of limit cycle solutions. In the model the feeding rate per unit predator per unit prey decreases as the prey become scare. The rigorous applicability of the perturbation technique depends on the assumptions that the limit cycle amplitude is relatively small and that near the equilibrium point the growth rate of each species is most sensitive to changes in the density of the other species. The second assumption is usually roughly satisfied in practice and examples are considered which suggest that the first assumption can be greatly relaxed.

Original languageEnglish (US)
Pages (from-to)291-299
Number of pages9
JournalBulletin of Mathematical Biology
Volume37
Issue number3
DOIs
StatePublished - Jun 1 1975

ASJC Scopus subject areas

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

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