Complex dynamics in a Filippov pest control model with group defense

In this paper, an integrated pest management Filippov model with group defense behavior is established, which takes the population density of pests as the control index of integrated pest management. First, under the condition that both subsystems have a globally asymptotically stable equilibrium, the dynamics of the established model are systematically analyzed, including the sliding mode dynamics, the existence and global stability of the real, virtual and pseudo equilibrium, as well as boundary-node and boundary-focus bifurcation. Next, we study the complex dynamics in the Filippov model when an unstable node (focus) or a stable limit cycle occurs in the subsystem by using numerical simulations. The results show that although there are no closed orbits in subsystem, a stable periodic solution may exist for Filippov system after switching perturbation. Finally, we conclude that the group defense behavior of pest makes it harder to control.