Existence of multiple sliding segments and bifurcation analysis of Filippov prey–predator model

In a prey–predator model, an effective management strategy called the threshold policy control (TPC) is proposed, resulting in Filippov system. Considering the limitation of environmental resources, Filippov system with the weighted sum as the index is put forward in the prey–predator model with Ivlev’s function response. Firstly, the existences of sliding segments in four cases have been discussed completely. Further, the sliding mode dynamics, the existences of different types of equilibria and tangent point, regular/virtual equilibrium and sliding mode bifurcations have been addressed. Moreover, the results obtained in present work indicate that the local sliding bifurcations such as boundary focus, boundary node and tangent bifurcations occur sequentially with the threshold value varying. Finally, some global sliding bifurcations including touching and buckling bifurcations are investigated by employing numerical techniques.