Theory and Numerics of Double-Vibrational Resonance in the Overdamped Oscillator

Vibrational resonance (VR) in the overdamped oscillator with a triple-well potential driven by a low-frequency force and a high-frequency force is investigated by using the method of direct separation of motion. An approximate analytical expression for the response amplitude Q is obtained. Based on the approximate analytical expression, the double VR is found. The positions of B (the amplitude of the high-frequency signal) and Ω (the frequency of the high-frequency signal) at which the VR occur are determined, and the relation between them are analyzed. The theoretical predictions are found to be in good agreement with the numerical results.