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Pramana

, 92:89 | Cite as

Vibrational resonance in a harmonically trapped potential system with time delay

  • Zhenglei Yang
  • Lijuan NingEmail author
Article
  • 16 Downloads

Abstract

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.

Keywords

Vibrational resonance time delay signal amplification harmonically trapped potential 

PACS Nos

05.45.−a 02.30.Ks 05.90.+m 46.40.Ff 

Notes

Acknowledgements

This work was supported by the Fundamental Research Funds for the Central Universities (Grant No. GK201701001).

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Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.School of Mathematics and Information ScienceShaanxi Normal UniversityXi’anChina

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