带有保护区域的加法Allee效应捕食-食饵模型的共存解

doi:10.6040/j.issn.1671-9352.0.2014.582

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (09): 88-94.doi: 10.6040/j.issn.1671-9352.0.2014.582

• 论文 • 上一篇

带有保护区域的加法Allee效应捕食-食饵模型的共存解

李海侠

宝鸡文理学院数学与信息科学学院, 陕西宝鸡 721013

收稿日期:2014-12-26 修回日期:2015-03-06 出版日期:2015-09-20 发布日期:2015-09-26
作者简介:李海侠(1977-),女,讲师,博士,研究方向为偏微分方程及计算可视化. E-mail:xiami0820@163.com
基金资助:
国家自然科学基金资助项目(11401356); 陕西省教育厅专项科研计划资助项目(14JK1035);宝鸡文理学院重点科研资助项目(ZK15039)

Coexistence solutions for a predator-prey model with additive Allee effect and a protection zone

LI Hai-xia

School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, Shaanxi, China

Received:2014-12-26 Revised:2015-03-06 Online:2015-09-20 Published:2015-09-26

摘要/Abstract

摘要： 讨论了一类带有保护区域和加法Allee效应的扩散捕食-食饵模型。首先讨论了平凡解和半平凡解的稳定性, 接着考察了非常数正解的不存在性, 最后运用全局分歧理论得到了非常数正解的存在性条件。研究结果表明,在弱Allee效应下,当扩散系数适当且参数满足一定条件时,两物种能共存而且共存解稳定;当扩散系数充分大时两物种不共存。

关键词: 保护区域, 加法Allee效应, 分歧理论

Abstract: A diffusive predator-prey model with additive Allee effect and a protection zone is discussed. Firstly, the stability of trivial and semi-trivial solutions is investigated. Secondly, the non-existence of non-constant positive solutions is determined. Finally, the existence of non-constant positive solutions is obtained by using the global bifurcation theory. Under weakly Allee effect, the results indicate that the two species will coexist and the coexistence solutions are stable when the diffusion coefficient is suitably chosen and the parameters satisfy certain conditions. Furthermore, the two species cannot coexist when the diffusion coefficients are sufficiently large.

Key words: protection zone, bifurcation theory, additive Allee effect

中图分类号:

O175.26

李海侠. 带有保护区域的加法Allee效应捕食-食饵模型的共存解[J]. 山东大学学报（理学版）, 2015, 50(09): 88-94.

LI Hai-xia. Coexistence solutions for a predator-prey model with additive Allee effect and a protection zone[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(09): 88-94.

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带有保护区域的加法Allee效应捕食-食饵模型的共存解

Coexistence solutions for a predator-prey model with additive Allee effect and a protection zone

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