Bifurcation and stability of a fractional-order maglev system with electromagnetic nonlinearity under cogging excitation and dual-delay feedback control.

Existing studies on fractional-order maglev systems under cogging excitation have mainly considered single-delay control or equivalent nonlinear models, while the combined influence of electromagnetic nonlinearity and dual-delay feedback remains insufficiently clarified. This paper establishes a two-degree-of-freedom fractional-order maglev train model incorporating electromagnetic nonlinearity, cogging excitation, and distinct time delays in the displacement and velocity feedback channels. An analytical-numerical framework is developed to obtain the primary-resonance responses, stability boundaries, and bifurcation evolution. The results show that the two delay channels play non-equivalent roles in reshaping the resonance branches and stability regions. Under the coupled effects of dual delays and electromagnetic nonlinearity, closed-loop frequency islands, multistable responses, and delay-enhanced chaotic instability are observed. Compared with the delay parameters, the fractional-order parameter has a weaker influence on the global dynamic pattern. These findings reveal the dominant role of delay coupling in the nonlinear evolution of maglev systems and provide guidance for delay compensation and control-parameter tuning.