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  

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

作　　者：吴瑞雯 刘秀湘[1] 

机构地区：[1]华南师范大学数学科学学院,广州510631

出　　处：《华南师范大学学报（自然科学版）》2017年第6期101-106,共6页Journal of South China Normal University(Natural Science Edition)

基　　金：广东省自然科学基金项目(S2012010010034;2016A030313426)

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,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.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 have experience Hopf bifurcation. Moreover,the 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.

关 键 词：ALLEE效应 HOPF分支 Bogdanov-Takens分支 捕食-食饵系统 时滞 

分 类 号：O175.13[理学—数学]