In this paper, we consider a nonautonomous predator–prey model with Holling type II schemes and a prey refuge. By applying the comparison theorem of differential equations and constructing a suitable Lyapunov function, sufficient conditions that guarantee the permanence and global stability of the system are obtained. By applying the oscillation theory and the comparison theorem of differential equations, a set of sufficient conditions that guarantee the extinction of the predator of the system is obtained.

中文翻译：

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具有Holling II型计划和避难所的非自治捕食系统的动态行为

在本文中，我们考虑具有Holling II型计划和食饵避难所的非自治捕食者—食饵模型。通过应用微分方程的比较定理并构造一个合适的Lyapunov函数，可以获得保证系统持久性和全局稳定性的充分条件。通过应用振荡理论和微分方程的比较定理，获得了一组足以保证系统的捕食者灭绝的充分条件。