The Qualitative Analysis of Two Species Predator-Prey Model with Holling’s Type Ⅲ functional Response

Chen Jun-ping; Zhang Hong-de

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Chen Jun-ping, Zhang Hong-de. The Qualitative Analysis of Two Species Predator-Prey Model with Holling’s Type Ⅲ functional Response[J]. Applied Mathematics and Mechanics, 1986, 7(1): 73-80.

Citation:

Chen Jun-ping, Zhang Hong-de. The Qualitative Analysis of Two Species Predator-Prey Model with Holling’s Type Ⅲ functional Response[J]. Applied Mathematics and Mechanics, 1986, 7(1): 73-80.

Citation:

Chen Jun-ping, Zhang Hong-de. The Qualitative Analysis of Two Species Predator-Prey Model with Holling’s Type Ⅲ functional Response[J]. Applied Mathematics and Mechanics, 1986, 7(1): 73-80.

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The Qualitative Analysis of Two Species Predator-Prey Model with Holling’s Type Ⅲ functional Response

Chen Jun-ping¹,
Zhang Hong-de²

1.
Chongqing University, Chongqing;
2.
Nachung Teachers College, Nachong

Received Date: 1984-08-10
Publish Date: 1986-01-15

Abstract

Abstract

This paper is denoted to the qualitative analysis of two species predator-prey model with Boiling's type Ⅲ functional response. Conditions for the global stability ofnontrivial 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.

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References(5)

References

[1]	Kazarinoff N.D.and P.van Den Driessche,A model predator-prey system with functional response,J Mathematical Biosciences(1978),125-134.
[2]	陈兰荪、井竹君,捕食者-食饵相互作用中微分方程的极限环存在性和唯一性,科学通报,299(1984)521-523.
[3]	Alan Hastings,Global stability in two species systems,J.Math.Biology 5(1978),399-403.
[4]	Goh B.S.and Nedlands,Global stability in two species interactions,Journal of Mathmatical Biology 3(1976),313-318.
[5]	叶恋谦等,《极限环论》,上海科学出版社(1984).