一个具有时滞和阶段结构的比率依赖型捕食系统的稳定性  

Stability Analysis on a Ratio-dependent Predator-prey Model with Time Delay and Stage Structure

作　　者：王玲书[1] 张雅南[1] 冯光辉[2] 

机构地区：[1]河北经贸大学数学与统计学学院,石家庄050061 [2]军械工程学院基础部,石家庄050003

出　　处：《工程数学学报》2016年第2期138-150,共13页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11101117);河北省教育厅基金(QN2014040);河北经贸大学基金(2015KYQ01)~~

摘　　要：本文研究一个具有时滞和捕食者、食饵均具有阶段结构的比率依赖型捕食系统的稳定性.通过分析特征方程,运用Hurwitz判定定理,讨论了该系统的非负边界平衡点和正平衡点的局部稳定性,并得到了Hopf分支存在的充分条件;通过构造辅助系统,运用单调迭代方法和比较定理,讨论了该系统的非负边界平衡点和正平衡点的全局稳定性,从而得到了该生态系统灭绝与永久持续生存的充分条件.In this paper, a ratio-dependent predator-prey model with time delay due to the gestation of the predator and stage structure for both the predator and the prey is investigated. By analyzing the characteristic equations and applying Hurwitz criterion, the local stability of a semi-trivial boundary equilibrium and a positive equilibrium are discussed, respectively. More-over, it is proved that the system undergoes a Hopf bifurcation at the positive equilibrium. By comparison arguments and iteration technique, the global stability of the semi-trivial boundary equilibrium and the positive equilibrium are addressed, respectively.

关 键 词：捕食系统 阶段结构 时滞 稳定性 HOPF分支 

分 类 号：O175[理学—数学]