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

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

详细信息

Stability and Bifurcation Analysis in a Delayed Predator-Prey System with Mate-Finding Allee Effect

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.
- 时滞
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.
- Time delay