具有阶段结构及无穷时滞的非自治Lotka-Volterra型捕食系统的持久性

摘要

研究在Cg空间上具有阶段结构及无穷时滞的非自治Lotka-Volterra型捕食者-食饵系统的持久性.通过构造Lyapunov函数证明系统正解的一致有界性,利用比较定理及分析右端泛函,在与Ch空间上具有阶段结构及无穷时滞的捕食系统的相同的条件下,得到具无穷时滞和阶段结构的非自治系统持久性生存与非持久性生存的充分性条件；得出结论:成年捕食者的死亡率和成年食饵的密度对捕食者-食饵系统的持久性起着十分重要的作用.%The persistence of nonautonomous Lotka-Volterra type stage structured predator-prey system with infinite delay on Cg space is studied.By constructing Lyapunov function,the ultimately boundedness of positive solutions for this ecosystem is investigated.By comparison theorem and analyzing the right-hand functional of the ecosystem,under the same conditions of predator-prey system with stage structure and infinite delay on Ch space,some sufficient conditions are derived for the persistence and non-persistence of nonautonomous ecosystem with infinite delay and stage structure.The obtained results show that death rate of mature predators and prey densities play a very important role on the persistence of predator-prey system.