Stability and Hopf Bifurcation of the Maglev System with Delayed Feedback Control

The nonlinear maglev system with delayed feedback control is considered in this paper. Linear stability of the system is investigated by analyzing the associated characteristic transcendental equation. The stability and direction of the Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem. Meanwhile, numerical simulations results are given to support the above theoretical predictions. It can be seen from the analysis that when the delay reaches the critical value, the maglev system will undergo a supercritical Hopf bifurcation and generate stable periodic oscillation.