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Global stability and existence of sliding bifurcations in Filippov type prey-predator model. (English) Zbl 1361.34051
Summary: 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
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