Abstract Magnetic bearings have a longer lifespan and lower maintenance costs due to the lack of direct contact between the rotor and the bearings and the lack of friction, and their design needs to be increased day by day. Magnetic bearings come in three types: inactive (PMB), active (AMB), and hybrid (HMB). In active bearings, unlike inactive bearings in which a permanent magnet is used, the magnetic force can be controlled. In this study, the Jeffcott rotor, which rotates the two ends of the rotor, which rotates at a speed of ω, was controlled by two magnetic four-pole bearings. The rotor is flexible and a rigid disk is placed on it to cause static noise on the disk to cause systemic stimulation and cause the rotor to be unstable. In order to keep the rotor geometric center at the origin of the coordinates at the center of the bearings, a current in excess of the systemʹs dynamic control current, called the bias current (i0), was generated to maintain the rotor weight in a 𝑦 direction in the electromagnets. The magnetic force generated by the magnetic poles is a nonlinear function of the currents flowing through the coils and the air distance between the poles and the axis. Also, the nonlinear behavior of the system in the presence of forces created by active magnetic bearings was investigated by modeling the system as a flexible shaft, which also considered centrifugal force and gravitational force, and by considering a PD controller, differential equations. Nonlinear motion was obtained. Then the equations in the direction of x, y were calculated using multiple scales using constant and variable control coefficients in Maple software. The jump diagrams were plotted with different control coefficients using the data from the equations and the jump range was determined. The findings showed that in the range of 〖0.00056