Analytical study of vibrational resonance in an overdamped bistable oscillator

The results of analytical study of vibrational resonance (VR) occurring in overdamped bistable system driven by two periodic signals with very different frequencies are presented. Approximate solutions for responses at the low-frequency as a function of the amplitude, and the frequency of the additional high frequency modulation which describe well the main features of vibrational resonance are obtained. Scaling laws for the gain factor and the switching threshold in VR are also found. Analytical results are compared with results of the numerical simulation, showing a good agreement.