一类具有年龄结构的捕食-食饵反应扩散恒化器模型  

A predator-prey reaction diffusion chemostat model with age structure

作　　者：张帅 王治国[1] ZHANG Shuai;WANG Zhiguo(School of Mathematics and Information Science,Shaanxi Normal University,Xi’an 710119,China)

机构地区：[1]陕西师范大学数学与信息科学学院,陕西西安710119

出　　处：《纺织高校基础科学学报》2020年第2期61-69,共9页Basic Sciences Journal of Textile Universities

基　　金：国家自然科学基金(61672021);陕西省自然科学基础研究计划项目(2014JM1003)。

摘　　要：为研究物种的死亡率对恒化器模型中物种生存状态的影响,提出一类具有年龄结构的捕食-食饵反应扩散恒化器模型。应用最值原理、一致持续性理论、分歧理论等方法,讨论了模型解的全局存在性,分析了模型半平凡解的稳定性以及解的一致持续性,给出模型稳态解以死亡率为分歧参数的全局分歧结构。结果表明:存在死亡率的临界值,当死亡率小于临界值时物种共存,超过临界值捕食者死亡。In order to study the effect of species mortality on the dynamic behavior of species in the chemostat model,a class of age-structured predator-prey reaction diffusion chemostat model is proposed.With the principle of maximum value,uniform persistence theory,bifurcation theory and other methods,the global existence of the model solution is discussed,the stability of the model′s semi-trivial solution and the consistent consistency of the solution are analyzed,and the global bifurcation structure of the model′s positive steady-state solution is given by applying bifurcation theory.The results show that there is a threshold for mortality,species coexist when the mortality is less than the threshold,and predators die above the threshold.

关 键 词：捕食-食饵模型 反应扩散方程 恒化器 死亡率 最值原理 一致持久性 分歧 

分 类 号：O175.26[理学—数学]