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浙江大学学报（理学版）
浙江大学学报（理学版）  2016, Vol. 43 Issue (2): 156-163    DOI: 10.3785/j.issn.1008-9497.2016.02.006
数学与计算机科学     
一类带有比率依赖型反应函数的捕食-食饵模型正解的存在性和多重性
李海侠
宝鸡文理学院数学与信息科学学院, 陕西宝鸡 721013
The existence and multiplicity of positive solutions for a predator-prey model with ratio-dependent type functional response
LI Haixia
Institute of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, Shaanxi Province, China
 全文: PDF(1782 KB)  
摘要： 讨论了一类带有Crowley-Martin和比率依赖反应函数的扩散捕食-食饵模型.首先利用局部分歧理论考察了系统关于强半平凡解处产生正解的存在性,再运用扰动理论得到了正解的稳定性.最后借助全局分歧理论和不动点指数理论给出了正解多重性的条件.
关键词： 捕食-食饵模型;  Crowley-Martin反应函数;  分歧;  扰动;  多解    
Abstract: A diffusive predator-prey model with Crowley-Martin and ratio-dependent type functional responses is considered. Firstly, the existence of positive solutions which are relative to the strong semi-trivial solutions is investigated based on the local bifurcation theory. Moreover, by use of the perturbation theory, we obtain the stability of positive solutions. Finally, multiple conditions of positive solutions are determined by resorting to the global bifurcation theory and fixed point index theory. Results have shown the existence of stable solutions and multiple solutions under certain conditions.
Key words: predator-prey model    Crowley-Martin functional response    bifurcation    perturbation    multiplicity
收稿日期: 2014-12-05 出版日期: 2016-03-12
CLC:  O175.26  
基金资助: 国家自然科学基金资助项目(11271236,11401356);中央高校基本科研业务费专项资金资助(GK201302025,GK201303008);陕西省教育厅专项科研计划资助项目(14JK1035);陕西省自然科学基础研究计划项目(2015JM1008);宝鸡文理学院重点科研项目(ZK15039).
作者简介: 李海侠(1977-),ORCID:http://orcid.org/0000-0002-6347-7565,女,副教授,博士,主要从事偏微分方程计算及其可视化研究,E-mail:xiami0820@163.com.
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引用本文:

李海侠. 一类带有比率依赖型反应函数的捕食-食饵模型正解的存在性和多重性[J]. 浙江大学学报（理学版）, 2016, 43(2): 156-163.

LI Haixia. The existence and multiplicity of positive solutions for a predator-prey model with ratio-dependent type functional response. Journal of ZheJIang University(Science Edition), 2016, 43(2): 156-163.

链接本文:

https://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2016.02.006    或    https://www.zjujournals.com/sci/CN/Y2016/V43/I2/156

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