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Applied Mathematics and Mechanics

, Volume 7, Issue 1, pp 77–86 | Cite as

The qualitative analysis of two species predator-prey model with Holling's type III functional response

  • Chen Jun-ping
  • Zhang Hong-de
Article

Abstract

This paper is denoted to the qualitative analysis of two species predator-prey model with Holling's type III functional response. Conditions for the global stability of nontrivial equilibrium points and conditions for the existence and uniqueness of limit cycles around the positive equilibrium point are obtained. The biological interpretations of these conditions are discussed. The authors believe that the conditions established in this paper are new to literature.

Keywords

Qualitative Analysis Mathematical Modeling Equilibrium Point Industrial Mathematic Functional Response 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Kazarinoff, N. D. and P. van Den Driessche, A model predator-prey system with functional response,J. Mathematical Biosciences (1978), 125–134.Google Scholar
  2. [2]
    Chen Lan-sun and Jing Zhu-jun, The existence and uniquence of cycles of differential equation for a predator-prey interactions,KEXUE TONGBAO,29, 9 (1984), 521–523. (in Chinese)Google Scholar
  3. [3]
    Alan Hastings, Global stability in two species systems,J. Math. Biology 5 (1978), 399–403.Google Scholar
  4. [4]
    Goh B. S. and Nedlands, Global stability in two species interactions,Journal of Mathematical Biology 3 (1976), 313–318.Google Scholar
  5. [5]
    Ye Yan-qian,Theory of Limit Cycles, Shanghai Science Press (1984). (in Chinese)Google Scholar

Copyright information

© Shanghai University of Technology (SUT) 1986

Authors and Affiliations

  • Chen Jun-ping
    • 1
  • Zhang Hong-de
    • 2
  1. 1.Chongqing UniversityChongqing
  2. 2.Nanchung Teachers CollegeNanchung

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