<p>This paper investigates the nonlinear horizontal vibration of a cold rolling system induced by the gyroscope precession effect-a critical yet underexplored issue affecting strip quality and rolling stability. A nonlinear dynamic model is developed by incorporating the axial excitation force and the elastic deformation of the work roll based on d’Alembert principles. The primary parametric resonance response, corresponding to the first Arnold tongue, is analyzed using the multi-scale method and validated experimentally. To further understand the systematic dynamic behavior, the homotopy analysis method is employed to trace the evolution of energy orbits, revealing bifurcation and jump phenomena as the frequency ratio varies. A devil’s staircase pattern emerges, indicating multiple frequency-locked regions. These nonlinear features are further validated through cell mapping techniques, which depict the transformation of modal energy manifolds. Moreover, by introducing active control inputs, a constraint space for control parameters is designed to induce amplitude death within the maximum Arnold tongue region. The findings contribute to a deeper understanding of the resonance mechanism and offer a theoretical basis for stabilizing precision cold rolling systems via nonlinear control strategies.</p>