Non-linear factors such as magnetic force and rub-impact force are comprehensively considered on the basis of the classic Jeffcott rotor system model, and the dynamic model of the magnetic bearing-rotor system is established. The dimensionless motion equation is obtained by introducing dimensionless parameters. The pattern types and distribution regions of adjacent fundamental periodic motions of the system are obtained based on multi-objective and multi-parameter co-simulation analysis, and the dynamic behaviour is analysed through three-dimensional bifurcation diagram, two-parameter bifurcation diagram, single-parameter bifurcation diagram and axis locus diagram. The reasonable matching range of parameters of system and speed ratio is obtained in this paper, which optimizes the structural parameter design of the rotor system and determines its reasonable and stable working interval.