Effect of Modulated Signals on Vibrational Resonance in a Harmonically Trapped Potential System

We consider a harmonically trapped potential system driven by modulated signals with two widely different frequencies ω and Ω, where Ω >> ω. The forms of modulated signals are amplitude modulated (AM) and frequency-modulated (FM) signals. An amplitude-modulated external signal is consisting of a low-frequency (ω) component and two high-frequencies (Ω + ω) and (Ω − ω) whereas the frequency modulated signal consisting of the frequency components such as f sinωt cos(g cosΩt) and f sin(g cosΩt) cosωt. Depending upon the values of the parameters in the potential function, an odd number of potential wells of different depths can be generated. We numerically investigate the effect of these modulated signals on vibrational resonance (VR) in single-well, three-well, five-well and seven-well potentials. Different from traditional VR theory in the present paper, the enhancement of VR is made by the amplitudes of the AM and FM signals. We show the enhanced response amplitude (Q) at the low-frequency ω, showing the greater number of resonance peaks and non-decay response amplitude on the response amplitude curve due to the modulated signals in all the potential wells. Furthermore, the response amplitude of the system driven by the AM signal exhibits hysteresis and a jump phenomenon. Such behavior of Q is not observed in the system driven by the FM signal.