具有Mate-Finding Allee效应的时滞捕食-食饵系统的稳定性与分支分析 |
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引用本文: | 吴瑞雯,刘秀湘.具有Mate-Finding Allee效应的时滞捕食-食饵系统的稳定性与分支分析[J].华南师范大学学报(自然科学版),2017,49(6):101-106. |
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作者姓名: | 吴瑞雯 刘秀湘 |
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作者单位: | 1.华南师范大学数学科学学院 |
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基金项目: | 广东省自然科学基金项目;广东省自然科学基金项目 |
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摘 要: | 讨论了具有比率依赖功能性反应和食饵受到Mate-finding Allee效应制约的时滞捕食-食饵系统的稳定性和分支分析. 以时滞量为分支参数, 证明当时滞量穿过一些临界值时, 系统会在正平衡点处经历~Hopf~分支, 并给出相关的数值模拟结果; 给出当系统经历Bogdanov-Takens分支时滞量需要满足的限制条件, 进而表明时滞对系统有很重要的影响.
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关 键 词: | 时滞 |
收稿时间: | 2016-08-08 |
Stability and Bifurcation Analysis in a Delayed Predator-Prey System with Mate-Finding Allee Effect |
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Abstract: | The stability and bifurcation analysis of a delayed ratio-dependent predator-prey system with a mate-finding Allee effect on prey is discussed. The delay is chosen as the bifurcation parameter and the system may experience ~Hopf~ bifurcation. Moreover, our results show that under some conditions the system has a Bogdanov-Takens singularity, which indicates that the delay has an important effect on the dynamical behaviors of the system. |
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