In this paper, a general Filippov-type predator-prey model with a refuge is presented. We propose a discontinuous predator-prey model incorporating a threshold policy by extending a general continuous predator-prey model. By employing the qualitative analysis theory related to Filippov systems, the necessary and sufficient conditions for the global asymptotical stability of a standard cycle, a touching cycle and a sliding cycle are obtained respectively. Furthermore, the sliding cycle is globally finite-time stable. Especially, several kinds of sliding bifurcations including boundary node bifurcation, boundary focus bifurcation and grazing bifurcation are studied. Moreover, two specific models are provided to verify the main results obtained from the general model.

本文提出了一种带有避难所的一般Filippov型捕食者—食饵模型。我们通过扩展一般的连续捕食者—猎物模型，提出了一种结合阈值策略的不连续捕食者—猎物模型。通过使用与Filippov系统有关的定性分析理论，分别获得了标准循环，接触循环和滑动循环的全局渐近稳定性的充要条件。此外，滑动周期是全局有限时间稳定的。特别是，研究了边界节点分叉，边界焦点分叉和放牧分叉等几种滑动分叉。此外，提供了两个特定模型来验证从通用模型获得的主要结果。