Estimates of predator-prey limit cycles

Donald L. De Angelis

Research output: Contribution to journalArticle

6 Citations (Scopus)

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

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Predator-prey
Limit Cycle
perturbation
predator
Prey
predators
Perturbation techniques
Growth
Estimate
Differential equations
Unit
Perturbation Technique
Predator-prey Model
Predator
Perturbation Method
Equilibrium Point
methodology
Differential equation
Decrease
Model

ASJC Scopus subject areas

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

Cite this

Estimates of predator-prey limit cycles. / De Angelis, Donald L.

In: Bulletin of Mathematical Biology, Vol. 37, No. 3, 01.06.1975, p. 291-299.

Research output: Contribution to journalArticle

De Angelis, Donald L. / Estimates of predator-prey limit cycles. In: Bulletin of Mathematical Biology. 1975 ; Vol. 37, No. 3. pp. 291-299.
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