基于Allee效应诱导的Filippov生态系统的动力学行为研究

覃文杰; 关海艳; 王培培; 唐光耀

doi:10.21656/1000-0887.400169

基于Allee效应诱导的Filippov生态系统的动力学行为研究

doi: 10.21656/1000-0887.400169

¹三峡大学三峡数学研究中心, 湖北宜昌 443002;²湖北民族大学数学系, 湖北恩施 445000

基金项目: 国家自然科学基金(11601268;11761031;11801311)

详细信息

作者简介:
覃文杰(1983—), 男, 副教授, 博士, 硕士生导师(E-mail: wenjieqin@hotmail.com)；关海艳(1986—), 女, 讲师, 博士(通讯作者. E-mail: ghyan928@ctgu.edu.cn).

中图分类号: O175
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出版历程
- 收稿日期: 2019-05-10
- 修回日期: 2019-07-12
- 刊出日期: 2020-04-01

Dynamic Behaviors of Filippov Ecosystems Induced by Allee Effects

¹Three Gorges Mathematical Research Center, China Three Gorges University, Yichang, Hubei 443002, P.R.China;²Department of Mathematics, Hubei Minzu University, Enshi, Hubei 445000, P.R.China

Funds: The National Natural Science Foundation of China(11601268; 11761031; 11801311)

摘要

摘要: 该文建立了一类由Allee效应诱导的非光滑Filippov切换系统.运用Filippov系统的定性分析方法，从理论上研究了系统的滑动区域、滑动模态和各类平衡点的存在性.同时用数值方法研究了系统的滑动模态分支、边界焦点分支及全局动力学行为.研究发现: Allee效应的强度可使种群的动态不稳定，不利于濒危生物种群的管理.
- Allee效应 /
- Filippov系统 /
- 滑动模态 /
- 滑动分支
Abstract: A non-smooth Filippov predatorprey system induced by Allee effects was proposed. The sliding domain, the sliding mode dynamics and the existence of several equilibria were discussed by means of the qualitative theory and method related to the Filippov system. Furthermore, the sliding mode bifurcation, the boundary focus bifurcation and the global dynamic behaviors were given through numerical simulations. The results indicate that, the intensity of Allee effects could make the dynamics of population become unstable, and may be unfavorable for the protection of endangered species.
- Allee effect /
- Filippov system /
- sliding mode /
- sliding bifurcation

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参考文献(17)

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