Pramana

, 90:49 | Cite as

Impact of depth and location of the wells on vibrational resonance in a triple-well system

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Abstract

The effect of depth and location of a triple-well potential on vibrational resonance is investigated in a quintic oscillator driven by a low-frequency force and a high-frequency force. The values of low-frequency \(\omega \) and amplitude g of the high-frequency force at which vibrational resonance occurs are derived both numerically and theoretically. It is found that: as \(\omega \) varies, at most one resonance takes place and the response amplitude at resonance depends on the depth and the location of the potential wells. When g is altered, the depth and location of wells can control the number of resonances, resulting in two, three and four resonances. The system parameters can be adjusted by controlling the depth and position of the wells to achieve optimum vibrational resonance. Furthermore, the changes induced by these two quantities in the tristable system are found to be richer than those induced in bistable systems.

Keywords

Vibrational resonance triple-well potential depth, location 

PACS Nos

46.40.Ff 05.45.−a 05.90.+ m 05.45.Pq 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11202120) and the Fundamental Research Funds for the Central Universities (Grant Nos GK201502007 and GK201701001).

References

  1. 1.
    P S Landa and P V E McClintock, J. Phys. A: Math. Gen33, L433 (2000)ADSCrossRefGoogle Scholar
  2. 2.
    J D Victor and M M Conte, Visual Neurosci17, 959 (2000)CrossRefGoogle Scholar
  3. 3.
    D C Su, M H Chiu and C D Chen, Precis. Eng18, 161 (1993)CrossRefGoogle Scholar
  4. 4.
    A O Maksimov, Ultrasonics 35, 79 (1997)CrossRefGoogle Scholar
  5. 5.
    A Knoblauch and G Palm, Biosystems  79, 83 (2005)CrossRefGoogle Scholar
  6. 6.
    M Gitterman, J. Phys. A: Math. Gen34, L355 (2001)ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    V N Chizhevsky and G Giacomelli, Phys. Rev. A  71, 011801 (2005)ADSCrossRefGoogle Scholar
  8. 8.
    V N Chizhevsky, E Smeu and G Giacomelli, Phys. Rev. Lett91, 220602 (2003)ADSCrossRefGoogle Scholar
  9. 9.
    V N Chizhevsky and G Giacomelli, Phys. Rev. E 77, 051126 (2008)ADSCrossRefGoogle Scholar
  10. 10.
    S Jeyakumari, V Chinnathambi, S Rajasekar and M A F Sanjuan, Int. J. Bifurc. Chaos  21, 275 (2011)CrossRefGoogle Scholar
  11. 11.
    T O Roylayinde, J A Laoye, O O Popoola and U E Vincent, Chaos  26, 093117 (2016)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    V Gandhimathi, S Rajasekar and J Kurths, Phys. Lett. A  360, 279 (2006)ADSCrossRefGoogle Scholar
  13. 13.
    B Deng, J Wang and X Wei, Chaos  19, 013117 (2009)ADSCrossRefGoogle Scholar
  14. 14.
    B Deng, J Wang, X Wei, K M Tsang and W L Chan, Chaos  20, 013113 (2010)ADSCrossRefGoogle Scholar
  15. 15.
    J Shi, C Huang, T Dong and X Zhang, Phys. Biol7, 036006 (2010)ADSCrossRefGoogle Scholar
  16. 16.
    A A Zaikin, L Lopez, J P Baltanas, J Kurths and M A F Sanjuan, Phys. Rev. E 66, 011106 (2002)ADSCrossRefGoogle Scholar
  17. 17.
    E Ullner, A Zaikin, J Garcia-Ojalvo, R Bascones and J Kurths, Phys. Lett. A 312, 348 (2003)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    I I Blekhman and P S Landa, Int. J. Non-linear Mech39, 421 (2004)ADSCrossRefGoogle Scholar
  19. 19.
    J H Yang and H Zhu, Chaos 22, 013112 (2012)ADSMathSciNetCrossRefGoogle Scholar
  20. 20.
    J H Yang, M A F Sanjuan, W Xiang and H Zhu, Pramana – J. Phys. 81, 943 (2013)Google Scholar
  21. 21.
    C Jeevarathinam, S Rajasekar and M A F Sanjuan, Chaos 23, 013136 (2013)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    D Hu, J Yang and X Liu, Commun. Nonlinear Sci. 17, 1031 (2012)CrossRefGoogle Scholar
  23. 23.
    G Gilboa, N Sochen and Y Y Zeevi, J. Math. Imaging Vision 20, 121 (2004)MathSciNetCrossRefGoogle Scholar
  24. 24.
    C Wagner and T Kiefhaber, Proc. Natl Acad. Sci. USA 96, 6716 (1999)ADSCrossRefGoogle Scholar
  25. 25.
    S Arathi and S Rajasekar, Phys. Scr. 84, 065011 (2011)ADSCrossRefGoogle Scholar
  26. 26.
    P K Ghosh, B C Bag and D S Ray, Phys. Rev. E 75, 032101 (2007)ADSCrossRefGoogle Scholar
  27. 27.
    S Rajasekar and M A F Sanjuan, Nonlinear resonances (Springer, 2016)CrossRefGoogle Scholar
  28. 28.
    P K Ghosh, B C Bang and D S Ray, J. Chem. Phys. 127, 044510 (2004)ADSCrossRefGoogle Scholar
  29. 29.
    F Bouthanoute, L El Arroum, Y Boughaleb and M Mazroui, Moroccan J. Condens. Matter  9, 17 (2007)Google Scholar
  30. 30.
    S Jeyakumari, V Chinnathambi, S Rajasekar and M A F Sanjuan, Chaos  19, 043128 (2009)ADSCrossRefGoogle Scholar
  31. 31.
    J H Yang and X B Liu, Chaos  20, 033124 (2010)ADSCrossRefGoogle Scholar
  32. 32.
    S Rajasekar, K Abirami and M A F Sanjuan, Chaos  21, 033106 (2011)ADSMathSciNetCrossRefGoogle Scholar
  33. 33.
    V N Chizhevsky, Phys. Rev. E  89, 062914 (2014)ADSCrossRefGoogle Scholar
  34. 34.
    S Rajasekar, S Jeyakumari, V Chinnathambi and M A F Sanjuan, J. Phys. A: Math. Theor.  43, 465101 (2010)ADSCrossRefGoogle Scholar
  35. 35.
    S Lenci, G Menditto and A M Tarantino, Int. J. Non-Linear Mech.  34, 615 (1999)CrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.School of Mathematics and Information ScienceShaanxi Normal UniversityXi’an China

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