一类具有阶段结构的非自治捕食者—食饵系统的研究

A predator-prey system with nonautonomous stage-structure

通过利用微分方程定性理论,证明一类具有阶段结构的非自治食饵—捕食者模型解的系统,在适当条件下是持久的。针对模型的周期系统,利用泛函分析的Brouwer不动点定理和构造Lyapunov泛函的方法,证明该系统正周期解存在且全局渐近稳定的充分条件;对更具普遍意义的概周期现象,得到了概周期正解存在且全局渐近稳定的充分条件。

In this paper,a predator-prey model with nonautonomous stage-structure was studied. It is proved by differential equationqualitative theory that the system was permanent under proper conditions. By Brouwer fixed point theory and constructing a suitable sufficient, Lyapunov function, the sufficient conditions were established for the global asymptotic stability of the periodic solution for the periodic system of the model. With respect to the general almost periodic system, we obtained the sufficient conditions for the existence of general periodic positive solution as well as globally asymptotic stability.