The most critical factor for increasing crop production is the successful resistance of pests and pathogens which has massive impacts on global food security. Therefore, Filippov systems have been used to model and grasp control strategies for limited resources in Integrated Pest Management (IPM). Extensive studies have been done on these systems where the evolution is governed by a smooth set of ordinary differential equations (ODEs). As far as we know the time delay has not been considered in these systems, which we mean that a set of delay differential equations (DDEs). With this motivation, a Filippov prey–predator (pest–natural enemy) model with time delay is introduced in this paper, where the time delay represents the change of growth rate of the natural enemy before releasing it to feed on pests. The threshold conditions for the stability of the equilibria are derived by using time delay as a bifurcation parameter. It is shown that when the time delay parameter passes through some critical values, a periodic oscillation phenomenon appears through Hopf bifurcation. Further, by employing Filippov convex method we obtain the equation of sliding motion and address the sliding mode dynamics. Numerically, we demonstrate that the time delay plays a substantial role in discontinuity-induced bifurcation. More precisely, one can get boundary focus bifurcation from boundary node bifurcation through variation of the value of the time delay. Moreover, the time delay is used as a bifurcation parameter to obtain sliding–switching and sliding–grazing bifurcations. In conclusion, a Filippov system with time delay can give new insights into pest control models.

作物增产的最关键因素是对害虫和病原体的成功抗药性，对全球粮食安全产生巨大影响。因此，Filippov系统已被用于建模和掌握病虫害综合防治（IPM）中有限资源的控制策略。已经对这些系统进行了广泛的研究，这些系统的演化受一组光滑的常微分方程（ODE）支配。据我们所知，在这些系统中尚未考虑时间延迟，这意味着一组延迟微分方程（DDE）。在这种动机下，本文引入了具有时滞的Filippov捕食者-天敌（害虫-天敌）模型，其中时滞表示天敌释放以害虫为食之前其生长速率的变化。通过使用时间延迟作为分叉参数来导出平衡稳定性的阈值条件。结果表明，当时延参数通过一些临界值时，通过霍普夫分叉出现周期性的振荡现象。此外，通过采用Filippov凸方法，我们获得了滑动运动方程并解决了滑模动力学问题。在数值上，我们证明了时间延迟在不连续性引起的分叉中起着重要作用。更准确地说，可以通过改变时延值从边界节点分叉得到边界焦点分叉。此外，将时间延迟用作分叉参数以获取滑动切换和滑动掠牧分叉。综上所述，