捕食者具有传染病的时滞捕食系统模型分析  

Time-Delay Predator-Prey Model with Disease in the Predator

作　　者：张拥军[1] 王美娟[1] 徐金瑞[1] 

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《复杂系统与复杂性科学》2009年第4期83-90,共8页Complex Systems and Complexity Science

摘　　要：提出了一类捕食者具有传染病的时滞生态-流行病模型。该模型中,捕食者和食饵均具有密度制约,并引入时滞对模型加以讨论。利用特征根法、函数分析法及线性化方法对模型动力学特性进行分析。证明了模型平衡点的存在性并分析其渐近稳定性,得出系统平衡点的渐近稳定性和Hopf分支存在的充分条件。A predator-prey model with disease in the predator is formulated and analyzed. Both prey and predator are density-dependent and the time delay is also been taken into consideration. By using eigen- value, function analysis and linearization, the dynamic characteristics of the model is presented in the paper. The existence of the equilibrium points is proved, and the sufficient conditions for the partial asymptotic stability of some equilibrium and the Hopf bifurcations are established.

关 键 词：平衡点 线性化 最大不变集 特征根法 生态-流行病模型 时滞 

分 类 号：O175.13[理学—数学]