具有同类相食的修正Leslie-Gower捕食-食饵扩散模型共存解的稳定性和唯一性  

Stability and Uniqueness of the Coexistence Solutions of a Modified Leslie Gower Predator-Prey Model with Cannibalism and Diffusion

作　　者：路银豆 李海侠 范示示 LU Yindou;LI Haixia;FAN Shishi(School of Mathematics and Information Science,Baoji University of Arts and Sciences,Baoji 721013,China)

机构地区：[1]宝鸡文理学院数学与信息科学学院,宝鸡721013

出　　处：《西安工业大学学报》2023年第5期413-419,469,共8页Journal of Xi’an Technological University

基　　金：国家自然科学基金项目(12061081,12001425);陕西省科技厅工业攻关项目(2022GY-071);宝鸡文理学院博士科研项目(ZK2018069)。

摘　　要：为了研究一类具有食饵同类相食的修正Leslie-Gower捕食-食饵扩散模型,文中利用不动点指数理论得到了共存解的存在条件,结合线性算子的扰动理论和不动点指数理论讨论了共存解的稳定性和唯一性。利用比较原理给出了抛物系统持久和灭绝的条件。通过数值模拟对理论结果进行了验证和补充。研究结果表明:当食饵的同类相食率较小且捕食者的最大增长率较大时食饵和捕食者持久共存,进而当食饵和捕食者间的相互作用强度充分小时系统存在唯一且稳定的共存解。The paper aims to study a modified Leslie-Gower predator-prey model with prey cannibalism and diffusion.The conditions for the existence of coexistence solutions are obtained by using the fixed point index theory.And then the stability and uniqueness of coexistence solutions are discussed based on both the perturbation theory of linear operators and the fixed point index theory.The conditions for permanence and extinction of the parabolic system are given by using the comparison theorem.Finally,numerical simulations are carried out to verify and complement the theoretical results.The research shows that the prey and predator can persistently coexist when the cannibalism rate of the prey is small and the maximal growth rate of the predator is large and that the system has only one unique linearly stable coexistence solution when the strength of intraspecific interaction between the prey and predator is sufficiently small.

关 键 词：捕食食饵模型 同类相食 不动点指数 稳定性 唯一性 

分 类 号：Q141[生物学—生态学] O175[生物学—普通生物学]