Dynamics and bifurcation analysis of a delay non-smooth Filippov Leslie-Gower prey-predator model

In this paper, we proposed a Filippov prey-predator model with time delay considering threshold policy control of integrated pest management. The study aims to address how the threshold and time delay influence the dynamics of the model. To do this, the existence and the stability of the equilibria of the subsystems have been explored, and then, we apply Filippov convex method to investigate the sliding domain and sliding mode dynamics. Furthermore, the complex dynamics including stability of equilibrium, sliding dynamics and various bifurcation phenomena with respect to time delay and economic threshold have been investigated in more detail. The system will display types of local (boundary node/focus bifurcation) and global bifurcations (touching, sliding switching and crossing bifurcations) if the time delay crosses some critical values, such that the pest management is challenged for the number of pests will exceed the given tolerant value. These results show how crucial in the pest control to consider time delay.