食饵患病且捕食者具有Crowley-Martin型功能反应函数的阶段结构捕食-食饵模型

Stage-Structured Predator-Prey Model with Diseased Prey and a Predator with a Crowley-Martin-Type Functional Response Function

研究食饵患病、捕食者具有阶段结构且捕食者的功能反应函数为Crowley-Martin型的捕食-食饵模型.文中假设疾病仅在食饵之间流行,捕食者同时捕获易感食饵和患病食饵.文中运用单调动力系统理论和构造Lyapunov泛函相结合的方法得到了模型中所有边界平衡点的全局渐近稳定性,其次运用一致持久生存理论得到了患病食饵一致持久生存的充分条件.最后,在数值模拟的部分不仅验证了文中定性理论分析的结果,同时将具有Crowley-Martin型功能反应函数的模型与具有Beddington-DeAngelis型功能反应函数的模型进行了对比分析,扩展了文中的定性理论分析结果.

This paper investigates a predator-prey model in which the prey is infected,the predator has a stage-structure and the predator's functional response function is of the Crowley-Martin type.It is assumed that the disease is only prevalent among prey and that the predator captures both susceptible and infected prey.In the paper,the global asymptotic stability of all boundary equilibria points in the model is obtained by combining monotone dynamical system theory and the construction of Lyapunov generalized functions.Secondly,we get the suficient conditions of uniform persistence for the infected prey by using the uniform persistence theory.Finally,in the numerical simulation part,not only the results of the qualitative theoretical analysis in the paper are verified,but also the model with Crowley-Martin type functional response function and the model with Beddington-DeAngelis type functional response function are compared and analyzed,which extends the results of the qualitative theoretical analysis in the paper.