一类具有时滞和阶段结构的食饵-捕食者模型的全局稳定性分析  

Global Stability of a Predator-prey Model with Time Delay and Stage Structure

作　　者：王丽丽[1] 徐瑞[1] 

机构地区：[1]军械工程学院应用数学研究所,河北石家庄050003

出　　处：《河北师范大学学报（自然科学版）》2014年第2期117-122,共6页Journal of Hebei Normal University：Natural Science

基　　金：国家自然科学基金(11071254);河北省青年自然科学基金(A2013506012);军械工程学院基础部科研基金(Jcky1302)

摘　　要：研究了一类具有时滞和阶段结构的食饵-捕食者模型.通过分析特征方程,讨论了非负边界平衡点和正平衡点的局部稳定性.利用无限维系统的持续性理论,得到了系统持久性的条件,并通过构造适当的Lyapunov泛函,得到了非负边界平衡点和正平衡点的全局渐近稳定的充分条件.A delayed predator-prey model with stage structure for predator is investigated. By analyzing the corresponding characteristic equations, the local stability of each of feasible equilibria of the system is discussed. By using the persistence theory on infinite dimensional systems, it is proven that the system is permanent if the coexistence equilibrium exists. By using Lyapunov functionals and LaSalle＇s invariance principle,sufficient conditions are received for the global asymptotic stability of the nonnegative boundary equilibria and the positive equilibrium.

关 键 词：时滞 阶段结构 食饵-捕食者模型 稳定性 

分 类 号：O175.13[理学—数学]