<p>Engineering equipment inevitably experiences external excitations during service, triggering resonance behavior. The energy transfer under multi-field coupling plays a critical role in governing structural dynamic stability. This study investigates the harmonic resonance and bifurcation of ferromagnetic functionally graded (FFG) cylindrical shells under magnetic and thermal fields. The theoretical model is developed by integrating thermoelastic theory and Donnell’s shell theory to derive the kinetic and strain energies. Based on the magnetoelastic theory, the dynamic eddy current Lorentz force and the static magnetization force are derived, enabling a mathematical description of the magnetically induced static–dynamic coupled loads. By means of Hamilton’s principle, geometric nonlinearity, nonlinear magnetization, and nonlinear thermoelastic deformation are incorporated into a unified modeling framework, yielding a multi-nonlinear dynamic model with spatial parameter dependence. By employing the method of multiple scales, the superharmonic and subharmonic resonance solutions are obtained analytically, and the dynamic stability is then assessed based on Lyapunov’s theory. Parametric analysis systematically evaluates how shell compositions and physical fields alter resonance and stability boundaries. Notably, with excitation amplitude and magnetic field intensity as bifurcation parameters, numerical simulations reveal the transition path between periodic motion and chaos.</p>