一个具有时滞和阶段结构的捕食模型的全局稳定性  

Global Stability of a Predator-Prey System with Time Delay and Stage Structure

作　　者：王玲书[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数学教研室,石家庄050003

出　　处：《工程数学学报》2013年第6期833-845,共13页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11071254;11101117)~~

摘　　要：本文研究了一个比率依赖的、捕食者和食饵均具有阶段结构的捕食者-食饵相互作用模型,并讨论了由捕食者种群的孕期所引起的时滞对种群动力学性态的影响.通过分析相应的特征方程,运用Hurwitz判定定理,文中分别给出了该模型的非负边界平衡点和正平衡点局部稳定的充分条件,并得到了Hopf分支存在的充分条件;运用单调迭代方法和比较定理,分别给出了该模型的非负边界平衡点和正平衡点的全局稳定的充分条件,从而得到了保证该生态系统永久持续生存或灭绝的充分条件.This paper studies 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. By analyzing the corresponding characteristic equations, sufficient conditions are given for the local stability of a boundary equilibrium and a positive equilibrium, respectively. Yhrthermore, it is proved that the system undergoes a Hopf bifurcation at the positive equilibrium. By using the iteration technique and comparison arguments, sufficient conditions are derived for the global stability of the boundary equilibrium and the positive equilibrium, respectively. As a result, the threshold is obtained for the permanence or extinction of the system.

关 键 词：捕食模型 时滞 阶段结构 持续生存 灭绝 

分 类 号：O175[理学—数学]