Some results on global stability of a predator-prey system

Kuo Shung Cheng*, Sze Bi Hsu, Song-Sun Lin

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

87 Scopus citations


In this paper we derive some results to ensure the global stability of a predator-prey system. The results cover most of the models which have been proposed in the ecological literature for predator-prey systems. The first result is very geometric and it is very easy to check from the graph of prey and predator isoclines. The second one is purely algebraic, however, it covers the defects of the first one especially in dealing with Holling's type-3 functional response in some sense. We also discuss the global stability of Kolmogorov's model. Some examples are presented in the discussion section.

Original languageEnglish
Pages (from-to)115-126
Number of pages12
JournalJournal of Mathematical Biology
Issue number1
StatePublished - 1 Jan 1982


  • Global stability
  • Predator-prey system

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