Sliding Bifurcation Analysis and Global Dynamics for a Filippov Predator-prey System

This paper studies a Filippov predator-prey system, where chemical control strategies are proposed and analyzed. Initially, the exact sliding segment and its domains are addressed. Then the existence and stability of the regular, virtual, pseudoequilibria and tangent points are discussed. It shows that two regular equilibria and a pseudoequilibrium can coexist. By employing theoretical and numerical techniques several kinds of bifurcations are investigated, such as sliding bifurcations related to the boundary node (focus) bifurcations, touching bifurcations, sliding crossing bifurcation and buckling bifurcations (or sliding switching). Furthermore, it makes comparison of the obtained results with previous studies for the Filippov predatorprey system without control strategies. Some biological implications of our results with respect to pest control are also given.