带时滞的Holling-Tanner比率依赖型捕食被捕食模型的triple-zero分支  

Triple zero Bifurcation of a Delayed Ratio-dependent Holling-Tanner Predator-prey System

作　　者：刘霞[1] 常红翠 焦建锋 

机构地区：[1]河南师范大学数学与信息科学学院大数据统计分析与优化控制河南省工程实验室,河南新乡453007

出　　处：《河南师范大学学报（自然科学版）》2017年第1期98-105,共8页Journal of Henan Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11601131;11501177);国家留学基金资助;河南省教育厅科学技术研究重点项目(17A110025;15A110034)

摘　　要：主要讨论了一类被捕食者带扰动项且具有常数率收获的时滞捕食被捕食系统的triple zero分支问题.首先得到了系统的平衡点是triple zero奇点的存在条件,随后将原系统开拆标准型的计算转化为一个新系统的四重零分支标准型问题,通过推广应用时滞微分方程的中心流形定理和标准型约化理论,推导出了原系统的triple zero分支的开拆标准型.In this paper,the triple zero bifurcation of a delayed predator prey system with prey refuge and constant rate harvesting is considered. Firstly,the existence conditions under which the interior equilibrium of the system is a triple zero singularity are obtained. Then,the computational problem of the unfolding normal form of original system is transformed to compute a quadruple zero bifurcation normal form of a new system,by generalizing and applying the center manifold theorem and normal form reduction theory of delay differential equations,the normal form of the triple zero bifurcation of the original system is derived.

关 键 词：捕食被捕食 时滞 TRIPLE zero分支 开拆标准型 

分 类 号：O175.1[理学—数学]