Global stability and existence of sliding bifurcations in Filippov type prey-predator model.

*(English)*Zbl 1361.34051Summary: This paper is concerned with a two species Filippov predator-prey model. In the model, the predator is provided with additional food as its density goes above a threshold value. The regular, virtual and pseudo-equilibrium points as well as boundary equilibrium and tangent points of the Filippov system are obtained and analyzed. Detailed analysis for transcritical bifurcation about axial points has been carried out. Also, the existence of Hopf bifurcation about the interior point has been established. Sliding mode dynamics is discussed. The regular/virtual equilibrium, boundary equilibrium and touching bifurcations have been discussed. The coexistence of virtual and pseudo equilibria are shown numerically. Pseudo-equilibrium is shown to be a saddle by means of numerical simulation.

##### MSC:

34C60 | Qualitative investigation and simulation of ordinary differential equation models |

34C23 | Bifurcation theory for ordinary differential equations |

92D25 | Population dynamics (general) |

92D40 | Ecology |

34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |

34D20 | Stability of solutions to ordinary differential equations |

34A36 | Discontinuous ordinary differential equations |