Stall spin is a hot topic in the field of flight dynamics in recent years. In order to solve the problem that conventional aerodynamic modeling and analysis are difficult to describe high angle of attack stall spin characteristics, the equilibrium point solution and stability analysis of the F-16 aircraft are carried out based on the bifurcation analysis method. With elevator deflection as a variable parameter, the global equilibrium solution of the aircraft and the relationship between its stability and elevator deflection are studied. A time domain simulation analysis of the aircraft model is carried out with an equilibrium state selected on the stall spin branch as the initial value, verifying the equilibrium and stability of the state. In addition, the entire stall spin entry to recovery is achieved by flight control. The simulation results show that the bifurcation analysis is very effective in studying the stall spin characteristics of aircraft at high angles of attack.