一类具有Allee效应的捕食-食饵扩散模型的全局分歧  

Global bifurcation for a diffusive predator-prey model with Allee effect and Holling-III functional response

作　　者：李海侠 LI Hai-xia(School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, Shaanxi, China)

机构地区：[1]宝鸡文理学院数学与信息科学学院

出　　处：《宝鸡文理学院学报（自然科学版）》2019年第2期1-4,10,共5页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：陕西省自然科学基础研究计划项目(2014JQ2-1003);陕西省教育厅专项项目(16JK1046);宝鸡市科技计划项目(2018JH-20);宝鸡文理学院博士科研项目(ZK2018069);渭南师范学院科研项目(16ZRRC05)

摘　　要：目的 研究一类具有Allee效应和Holling-III型反应函数的捕食-食饵扩散模型,从而有望为具有Allee效应的捕食-食饵模型的研究提供理论基础。方法 采用极值原理和简单特征值的分歧理论思想。结果 得到了系统共存解的全局存在条件。结论 研究表明在强Allee效应和适当条件下捕食者和食饵共存。Purposes-To provide theoretical basis for the research of the predatox-prey model with Allee effect by studying a diffusive predator-prey model with Alice effect and Holling-III functional response. Methods-The thought of the maximum principle and bifurcation theory from a simple eigenvalue is adopted. Result-The global existence conditions of coexistence solution for the model are obtained. Conclusion-The research shows that predator and prey will coexist under strong Allee effect and appropriate conditions.

关 键 词：捕食-食饵扩散模型 强Allee效应 分歧理论 全局存在性 

分 类 号：O175.26[理学—数学]