具有修正的Lelie-Gower项Holling-III类时滞捕食系统的Hopf分支

张子振; 杨慧中

doi:10.3724/SP.J.1004.2013.00610

具有修正的Lelie-Gower项Holling-III类时滞捕食系统的Hopf分支

doi: 10.3724/SP.J.1004.2013.00610

张子振^1,2,
杨慧中^1,

1.
江南大学教育部轻工过程先进控制重点实验室无锡 214122
2.
安徽财经大学管理科学与工程学院蚌埠 233030

详细信息

通讯作者:
杨慧中

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出版历程
- 收稿日期: 2012-05-16
- 修回日期: 2013-03-19
- 刊出日期: 2013-05-20

Hopf Bifurcation in a Delayed Predator-prey System with Modified Leslie-Gower and Holling-type III Schemes

ZHANG Zi-Zhen^1,2,
YANG Hui-Zhong^1
,

1.
Key Laboratory of Advanced Process Control for Light Industry (Ministry of Education), Jiangnan University, Wuxi 214122, China;
2.
School of Management Science and Engineering, Anhui University of Finance and Economics, Bengbu 233030, China

摘要

摘要: 研究了一类具有修正的Leslie-Gower项与Holling-III类功能性反应函数的时滞捕食系统. 以时滞为分支参数, 讨论系统正平衡点的局部稳定性, 给出系统产生Hopf分支的时滞关键值. 进一步, 确定系统Hopf分支的方向与分支周期解稳定性, 并对系统全局分支周期解的存在性进行讨论. 最后, 利用仿真实例验证理论分析结果的正确性.
- 捕食系统, 时滞, 稳定性, 分支, 周期解
Abstract: In this paper, we consider a predator-prey system with modified Leslie-Gower and Holling type III schemes. By regarding the time delay as the bifurcation parameter, the local asymptotic stability of the positive equilibrium is investigated. And we find that Hopf bifurcations can occur as the time delay crosses some critical values. In particular, special attention is paid to the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions. In addition, the global existence of periodic solutions bifurcating from the Hopf bifurcation are considered by applying a global Hopf bifurcation result. Finally, numerical simulations are carried out to illustrate the main theoretical results.
- Predator-prey, time delay, stability, bifurcation, periodic solution

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参考文献(1)

[1]

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