Global dynamics of a predator-prey system with density-dependent mortality and ratio-dependent functional response

In this paper, we study the global dynamics of a density-dependent predator-prey system with ratio-dependent functional response. The main features and challenges are that origin model is degenerate equilibrium higher order there multiple positive equilibria. Firstly, local qualitative behavior around explicitly described. Then, based on other equilibria, analysis carried out. Finally, existence Bogdanov-Takens bifurcation (cusp case) codimension two analyzed. This shows undergoes various phenomena, including saddle-node bifurcation, Hopf homoclinic along different topological sectors near origin. Numerical simulations presented to illustrate theoretical results.