具双Allee效应的时滞捕食系统的余维3分支分析

doi:10.3969/j.issn.1000-5641.2022.02.004

华东师范大学学报（自然科学版） ›› 2022, Vol. 2022 ›› Issue (2): 24-33.doi: 10.3969/j.issn.1000-5641.2022.02.004

具双Allee效应的时滞捕食系统的余维3分支分析

焦建锋(), 陈灿*()

郑州航空工业管理学院数学学院, 郑州　450046

收稿日期:2020-10-26 出版日期:2022-03-25 发布日期:2022-03-28
通讯作者: 陈灿 E-mail:jfjiaomath@zua.edu.cn;canchen1989@yeah.net
作者简介:焦建锋, 男, 博士, 讲师, 研究方向为种群动力学. E-mail: jfjiaomath@zua.edu.cn
基金资助:
国家自然科学基金(11801528); 河南省高等学校重点科研项目(22A110023)

Codimension 3 bifurcation of a delayed predator-prey system with double Allee effect

Jianfeng JIAO(), Can CHEN*()

School of Mathematics, Zhengzhou University of Aeronautics, Zhengzhou　450046, China

Received:2020-10-26 Online:2022-03-25 Published:2022-03-28
Contact: Can CHEN E-mail:jfjiaomath@zua.edu.cn;canchen1989@yeah.net

摘要/Abstract

摘要：

通过推广使用泛函微分方程的中心流形定理和规范型理论, 一类具有时滞和Allee效应的捕食系统的高余维分支问题被研究. 首先, 给出了正平衡点及余维3分支在此点处存在的充分条件. 然后, 推导出了系统在该正平衡点处的开拆规范型. 最后, 由规范型与原系统的拓扑等价性分析出原系统在正平衡点处出现的分支现象.

关键词: 捕食系统, 时滞, 三重零分支, Allee 效应

Abstract:

By generalizing and using the normal form theory and center manifold theorem of delay differential equations, a class of high-codimension bifurcation problems of predator-prey systems with delay and Allee effect are investigated. Firstly, sufficient conditions for the existence of the positive equilibrium and the codimension 3 bifurcation at this positive equilibrium are established. Subsequently, the normal form of the system at the positive equilibrium is deduced. Finally, from the topological equivalence of the normal form and the original system, the bifurcation phenomenon of the original system at the positive equilibrium is analyzed.

Key words: predator-prey system, delay, triple-zero bifurcation, Allee effect

中图分类号:

O175.12

焦建锋, 陈灿. 具双Allee效应的时滞捕食系统的余维3分支分析[J]. 华东师范大学学报（自然科学版）, 2022, 2022(2): 24-33.

Jianfeng JIAO, Can CHEN. Codimension 3 bifurcation of a delayed predator-prey system with double Allee effect[J]. Journal of East China Normal University(Natural Science), 2022, 2022(2): 24-33.

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具双Allee效应的时滞捕食系统的余维3分支分析

Codimension 3 bifurcation of a delayed predator-prey system with double Allee effect

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