Computer Engineering and Applications ›› 2016, Vol. 52 ›› Issue (15): 49-54.

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Predator-prey model with B-D functional response and stage structure

SONG Yan, XU Dongfang, LI Ang   

  1. College of Mathematics and Physics, Bohai University, Jinzhou, Liaoning 121000, China
  • Online:2016-08-01 Published:2016-08-12

具有阶段结构及B-D功能反应的食饵-捕食模型

宋  燕,胥东方,李  昂   

  1. 渤海大学 数理学院,辽宁 锦州 121000

Abstract: Stability of a predator-prey model with Beddington-DeAngelis functional response and stage structure for the prey is investigated. By the method of characteristic, the local stability of a predator-extinction equilibrium and a coexistence equilibrium of the model is discussed. By introducing a new lemma and applying the comparison principle of differential equation and iterative method, respectively, sufficient conditions are obtained for the global stability of the predator-extinction equilibrium and the coexistence equilibrium. Finally, numerical simulations are carried out to illustrate the main results.

Key words: stage structure, time delay, Beddington-DeAngelis functional response, predator-prey model, stability

摘要: 研究一类食饵具有阶段结构及Beddington-DeAngelis功能反应的食饵-捕食模型的稳定性,利用特征根法,讨论了捕食者灭绝平衡点及食饵和捕食者共存平衡点的局部稳定性;通过引入新的引理,利用微分方程比较定理及迭代法,得到了捕食者灭绝平衡点和食饵、捕食者共存平衡点全局稳定的充分条件;数值模拟验证了主要结果。

关键词: 阶段结构, 时滞, Beddington-DeAngelis功能反应, 食饵-捕食模型, 稳定性