Journal of Mathematical Biology

, Volume 12, Issue 1, pp 115–126

Some results on global stability of a predator-prey system

  • Kuo-Shung Cheng
  • Sze-Bi Hsu
  • Song-Sun Lin


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.

Key words

Global stability Predator-prey system 


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Copyright information

© Springer-Verlag GmbH & Co KG 1981

Authors and Affiliations

  • Kuo-Shung Cheng
    • 1
  • Sze-Bi Hsu
    • 1
  • Song-Sun Lin
    • 1
  1. 1.Department of Applied MathematicsNational Chiao Tung UniversityHsin-ChuTaiwan 300, Republic of China

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