Stabilization and de-stabilization of predator-prey systems under harvesting and nutrient enrichment

Fred Brauer, A. C. Soudack, H. S. Jarosch

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

A predator-prey system is modelled by a pair of ordinary differential equations, and the qualitative effects of prey nutrient enrichment and predator harvesting on the stability of the system are studied. Some theoretical analysis concerning the existence of equilibrium points and limit cycles is included. Three models are examined as examples and the concept of practical stability is introduced. For one of the models, computer simulations are included to illustrate the changes in qualitative behaviour under nutrient enrichment and harvesting. The results indicate that care must be taken in harvesting to prevent extinction of the predator and a resulting collapse of the entire ecosystem. This study should, therefore, prove to be a useful tool in resource management and control.

Original languageEnglish (US)
Pages (from-to)553-573
Number of pages21
JournalInternational Journal of Control
Volume23
Issue number4
DOIs
StatePublished - Jan 1 1976
Externally publishedYes

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Predator prey systems
Nutrients
Stabilization
Ordinary differential equations
Ecosystems
Computer simulation

ASJC Scopus subject areas

  • Computer Science Applications
  • Control and Systems Engineering

Cite this

Stabilization and de-stabilization of predator-prey systems under harvesting and nutrient enrichment. / Brauer, Fred; Soudack, A. C.; Jarosch, H. S.

In: International Journal of Control, Vol. 23, No. 4, 01.01.1976, p. 553-573.

Research output: Contribution to journalArticle

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