Discontinuous harvesting policy in a Filippov system involving prey refuge

In this article, we discuss sustainable harvesting using a Filippov predator–prey system, which can produce yield and at the same time prevent over-exploitation of bioresources. The model is composed of two subsystems and the dynamics switch from one to the other with the help of a switching condition. We have derived possible equilibria, their existence and stability conditions for the respective subsystems, along with a comprehensive analysis of their phase space. The local and global stability analysis of the two subsystems, with and without harvesting, are studied. Furthermore, for the Filippov system, we have performed bifurcation analysis for several key parameters like predation rate, threshold quantity and prey refuge. Some local and global sliding bifurcations are also observed for the system. The system is shown to have multiple stable steady states or multiple stable sliding cycles for some suitable choice of parameters. Numerical simulations are presented to illustrate the dynamical behaviour of the system.