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