Vibrational resonance in a Toda oscillator with higher-order nonlinear damping

This work investigates the phenomenon of vibrational resonance (VR) in an asymmetric Toda oscillator subjected to higher-order nonlinear damping and driven by dual periodic forces. First, using the method of direct separation of motions, the low-frequency response amplitude of the system is derived analytically. Second, the role of the damping coefficients in inducing VR and shaping the resonance peaks is examined. It is demonstrated that adjusting the higher-order damping parameters, particularly the quartic damping coefficient, can initiate and significantly enhance the resonance within specific parameter ranges. Third, the theoretical conditions for the onset of VR are established, and the parameter regime that supports double resonance peaks is explicitly determined. These analytical predictions are in excellent agreement with the results obtained from both numerical simulations and circuit simulations. The findings reveal that the resonance arises from a dynamical transition from periodic to quasiperiodic motion, which is central to the mechanistic understanding and potential control of nonlinear responses in damped systems.