Analysis and Bifurcations of Non-smooth Filippov Predator Prey System with Harvesting

In this study, it is assumed that harvesting is permitted only when the ratio of prey to predator is below a threshold value. The Filippov type dynamical system consisting of two smooth subsystems is investigated. The existence of harvesting factor within an interval dependent on biologically parameters of the system would ensure the existence and stability of interior equilibrium state for the harvested system. The boundary that splits the two subsystems is classified into sliding and crossing region. It is also proved that there does not exist any escaping region on the boundary. Different equilibrium points such as boundary points, tangent points, pseudo-equilibrium points are found out for the boundary. The visibility condition for these tangent points is determined. Boundary bifurcation and sliding bifurcation of the Filippov system are demonstrated numerically. The half saturation rate of predators plays a crucial role in determining whether the system to lie in specific sub-regions or is oscillating in between the two regions.