具有一般比率依赖功能性反应的阶段结构捕食系统性态分析
Dynamical Analysis of a Stage-Structured Predator-Prey System with General Ratio-Dependent Functional Response
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摘要: 考虑比率依赖的食饵带阶段结构捕食系统. 在假设食饵种群中未成年个体和成年个体由一个确定的年龄来划分开, 并且捕食者仅捕食未成年食饵的基础上, 讨论了平衡点的存在性. 由于系统在原点处不能线性化, 局部渐近稳定性分析运用了线性化和系统变换的方法. 此外, 还证明了当正平衡点存在时系统是一致持续生存的, 并利用极限系统理论和杜拉克判据研究了边界平衡点全局渐近稳定性, 这表明了此时捕食者种群将绝灭.Abstract: In this paper, we consider a ratio-dependent predator-prey system with a stage structure for the prey. It is assumed that immature and mature individuals of the prey population are divided by a fixed age and that the predator individuals only prey on the immature prey individuals. Existence of equilibria is discussed and their local asymptotical stability is analyzed by linearization and system transforming since the system cannot be linearized at the origin. It is shown that the system is uniformly persistent when positive equilibrium exists. And the global asymptotical stability of boundary equilibrium, which implies the extinction of the predator population, is studied by the limit system theory and Dulac criterion.
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