具功能性反应的食饵-捕食者两种群模型的定性分析
The Qualitative Analysis of Two Species Predator-Prey Model with Holling’s Type Ⅲ functional Response
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摘要: 本文对具Holling Ⅲ型功能性反应的食饵-捕食者两种群微分方程模型进行定性分析,得到了非平凡平衡点全局稳定性的条件,正平衡点周围存在唯一极限环的条件;同时,对这些条件的生态意义加以讨论。作者们相信这些条件在文献中还是新的。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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[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). -
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