一个具有时滞和捕食者、食饵均具有阶段结构的捕食模型  

A Predator-prey System with Time Delay and Stage Structure for the Predator and the Prey

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》2015年第1期72-84,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)~~

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捕食模型的稳定性.首先,通过分析特征方程,运用Hurwitz判定定理,分别给出了该模型的边界平衡点和正平衡点局部稳定的充分条件,并得到了该模型在正平衡点存在Hopf分支的充分条件;其次,运用无穷维动力系统的一致生存定理,得到了该模型持续生存的充分条件;最后,通过构造适当的Lyapunov泛函,运用La Sall不变集原理,分别给出了该模型边界平衡点和正平衡点全局稳定的充分条件.The stability of a predator-prey model with time delay and stage structure for both the predator and the prey is investigated. By analyzing the corresponding characteristic equations, su？cient conditions are given respectively for the local stability of each of feasible equilibria of the system and the existence of a Hopf bifurcation at the positive equilibrium. By means of the persistence theory on infinite dimensional systems, it is proven that the system is permanent if the positive equilibrium exists. By using the Lyapunov functions and the LaSalle invariant principle, su？cient conditions are derived respectively for the global stability of each of feasible equilibria of the model.

关 键 词：捕食模型 时滞 阶段结构 全局稳定 

分 类 号：O175.1[理学—数学]