一类空间退化的捕食-食饵模型的全局分歧结构

doi:10.6040/j.issn.1671-9352.0.2017.580

山东大学学报（理学版） ›› 2018, Vol. 53 ›› Issue (4): 76-84.doi: 10.6040/j.issn.1671-9352.0.2017.580

一类空间退化的捕食-食饵模型的全局分歧结构

董亚莹

西安工程大学理学院, 陕西西安 710048

收稿日期:2017-11-14 出版日期:2018-04-20 发布日期:2018-04-13
作者简介:董亚莹(1987— ), 女, 博士, 讲师, 研究方向为偏微分方程. E-mail:sxsbjsying@163.com
基金资助:
中国博士后科学基金资助项目(2016M602627);西安工程大学博士启动资金(BS1618)

Global bifurcation structure in a predator-prey model with a spatial degeneracy

DONG Ya-ying

School of Science, Xian Polytechnic University, Xian 710048, Shaanxi, China

Received:2017-11-14 Online:2018-04-20 Published:2018-04-13

摘要/Abstract

摘要： 研究了一类空间退化异质环境中带有Holling II型反应函数的捕食-食饵模型。当食饵的生长率较弱时, 通过比较原理给出了任意正稳态解的先验估计, 再利用全局分歧理论证明了正稳态解集合形成一条有界的全局分歧曲线;当食饵的生长率较强时, 通过反证法得到了任意正稳态解的先验估计, 并利用全局分歧理论证明了正稳态解集合形成一条无界的全局分歧曲线。

关键词: 先验估计, 全局分歧, Holling II, 空间退化

Abstract: A predator-prey model with Holling type II response function in a spatially degenerate heterogeneous environment is studied. When the prey growth rate is weak, a priori estimates of any positive steady-state solution is first obtained by the comparison principle, and then we show that the set of positive steady-state solutions forms a bounded global bifurcation curve by the global bifurcation theory. When the prey growth rate is strong, a priori estimates of any positive steady-state solution is first obtained by using reduction to absurdity, and then we show that the set of positive steady-state solutions forms an unbounded global bifurcation curve by the global bifurcation theory.

Key words: Holling II, global bifurcation, a priori estimates, spatial degeneracy

中图分类号:

O175.26

董亚莹. 一类空间退化的捕食-食饵模型的全局分歧结构[J]. 山东大学学报（理学版）, 2018, 53(4): 76-84.

DONG Ya-ying. Global bifurcation structure in a predator-prey model with a spatial degeneracy[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(4): 76-84.

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一类空间退化的捕食-食饵模型的全局分歧结构

Global bifurcation structure in a predator-prey model with a spatial degeneracy

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