We analyze the vibrational resonance in the Duffing oscillator system in thepresence of (i) a gamma distributed time-delayed feedback and (ii) integrativetime-delayed (uniformly distributed time delays over a finite interval)feedback. Particularly, applying a theoretical procedure we obtain anexpression for the response amplitude $Q$ at the low-frequency of the drivingbiharmonic force. For both double-well potential and single-well potentialcases we are able to identify the regions in parameter space where either (i)two resonances, (ii) a single resonance or (iii) no resonance occur.Theoretically predicted values of $Q$ and the values of a control parameter atwhich resonance occurs are in good agreement with our numerical simulation. Theanalysis shows a strong influence of both types of time-delayed feedback onvibrational resonance.
展开▼
