This paper is focussed on investigating the effect of linear time delay on vibrational resonance of a harmonically trapped potential system driven by a biharmonic external force with two wildly different frequencies \(\omega \) and \(\Omega \) with \(\omega \ll \Omega \). Firstly, the approximate analytical expression of the response amplitude Q at the low-frequency \(\omega \) is obtained by means of the direct separation of the slow and fast motions, and then we verified the numerical simulation by using the fourth-order Runge–Kutta method and found that it is in good agreement with the theoretical analysis. Next, the influence of the time-delay parameters on the vibrational resonance are discussed. There are some meaningful conclusions. If \(\tau \) is a controllable parameter, the response amplitude Q not only exhibits periodicity but also can be amplified via the cooperation of F and \(\tau \). If the time-delay intensity parameter r is a controllable parameter, the response amplitude Q is found to be much larger than that in the absence of time delay. Moreover, adjusting r can result in a better response than adjusting \(\tau \). This undoubtedly gives us a superior way to amplify the weak low-frequency signal.
Vibrational resonance time delay signal amplification harmonically trapped potential
05.45.−a 02.30.Ks 05.90.+m 46.40.Ff
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This work was supported by the Fundamental Research Funds for the Central Universities (Grant No. GK201701001).
V Mironov and V Sokolov, Radiotekh Elektron. 41, 1501 (1996)Google Scholar