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Magnetic liquid double suspension bearing (MLDSB) includes electromagnetic system and hydrostatic system, and the bearing capacity and stiffness can be greatly improved. It is very suitable for the occasions of medium speed, heavy load, and starting frequently. Due to the mutual coupling and interaction between electromagnetic system and hydrostatic system, the probability and degree of static bifurcation are greatly increased and the operation stability is reduced. And flow of bearing cavity, coil current, oil film thickness, and galvanized layer thickness are the key parameters to ensure operation safe and stable, which has an important influence on the static bifurcation behavior. So this article intends to establish the coupling model of MLDSB to reveal the range of parameter combination in the case of static bifurcation. The influences of different parameter groups on the singularity characteristics, phase trajectory, x − t curves, and suction basin of the single DOF bearing system are analyzed. The result shows that there are nonzero singularities and static bifurcation occurs when ε 2 > 0 or δ 2 > 0. As the flow of bearing cavity, coil current, oil film thickness, and galvanized layer thickness changes in turn, the singularities will convert between stable focus, unstable focus, stable node, and saddle point, and then the stable limit cycle may be generated. The attractiveness of singularity will change greatly with the flow of the bearing cavity and coil current changes slightly in the case of small current or large flow. The minimal change of galvanized layer thickness will lead to the fundamental change of the final stable equilibrium point of the rotor, while the final equilibrium point is slightly affected by the oil film thickness. This study can provide a reference for the supporting stability of MLDSB. [ABSTRACT FROM AUTHOR]