Multiple stabilities analysis in a magnetic bearing system with time delays

A kind of magnetic bearing system with time delay is considered. Firstly, multiple stabilities of the model is investigated. According to the analysis results, the bifurcation diagram is drawn in the appropriate parameter plane. Then the center manifold reduction and normal form computation for simple zero singularity are performed and detailed bifurcation analysis are carried out. Finally, some numerical simulations are presented to illustrate the results found.