Taking the unbalanced rotor system supported by rolling bearings as the research object, the variable step size Runge-Kutta method is used for numerical integration to obtain the dynamic response of the rotor system. According to the bifurcation diagrams, phase portraits and Poincaré maps under different conditions of increasing and decelerating, the bifurcation of coexisting attractor is analyzed, and the evolution process of its attraction region with the system parameters was revealed. The results show that when Hopf bifurcation, jump bifurcation and doubling bifurcation occur in the system with the change of rotating speed, there will be the coexistence of attractors. The jump bifurcation will lead to a sudden change in the topological structure of the basin of attraction, while the Hopf bifurcation and the doubling bifurcation have little effect on the basin of attraction. The research results can provide guidance for the operation of the system at different speeds, and provide theoretical basis for the smooth operation of the rolling bearing rotor system.