摘要
研究了一类食饵带有加法Allee效应的捕食-食饵模型共存解的存在性和稳定性.首先,利用局部分歧理论,分别以食饵和捕食者的出生率为分歧参数,得到了发自半平凡解的局部分歧解;其次,利用全局分歧理论,将局部分歧进行延拓并分析了全局分歧解的整体走向,从而得到了正解存在的充分条件;再次,讨论了局部分歧解的稳定性;最后,应用数值模拟技术验证并补充了一些理论结果.结果表明,当参数满足一定条件时,两物种可共存且共存解稳定.
In this paper,the existence and stability of coexistence solutions for a predator-prey diffusive model with additive Allee effect on prey have been investigated.Firstly,applying local bifurcation theory,local bifurcation solutions have been obtained which emanate from the semi-trivial solutions by regarding the birth rate of prey and predator as bifurcation parameters,respectively.Secondly,the local bifurcation has been extended by global bifurcation theory,and its trend been derived.Moreover,the sufficient conditions for the existence of positive solutions have been got.Thirdly,the stability of local bifurcation solutions has been discussed.Finally,some theoretical results have been verified and supplemented by the numerical simulation technique.The results indicate that the two species will coexist and the coexistence solutions are stable when the parameters satisfy certain conditions.
作者
代净玉
李艳玲
DAI Jing-yu;LI Yan-ling(School of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710119, China;Linyi No.1 Middle School, Linyi Shandong 276000, China)
出处
《西南师范大学学报（自然科学版）》
CAS
北大核心
2020年第11期6-17,共12页
Journal of Southwest China Normal University(Natural Science Edition)
基金
国家自然科学基金项目(61672021).
