, 93:102 | Cite as

Vibrational resonance in a higher-order nonlinear damped oscillator with rough potential

  • J A Laoye
  • T O Roy-Layinde
  • K A Omoteso
  • O O Popoola
  • U E VincentEmail author


We examine the vibrational resonance (VR) of particles moving in a strongly nonlinear damped medium with a harmonically perturbed potential consisting of a background smooth triple-well potential superimposed by a fast oscillating periodic function and subjected to weak and high-frequency (HF) driving forces. The combined effects of the nonlinear damping inhomogeneity and roughness induced by the harmonic perturbation on the phenomenon of VR were theoretically and numerically analysed. It was found that damping inhomogeneity contributed significantly to the enhancement of resonant states, while potential roughness can be optimised by the HF signal to assist resonance enhancement. Furthermore, the traditional smooth VR shapes occurring in the absence of roughness experienced significant distortion occasioned by potential roughness manifesting as spikes that could ultimately be optimised by large amplitudes of the fast signal to energetically facilitate the potential barrier crossing process, thereby enabling VR enhancement.


Oscillations vibrations fluctuations resonance nonlinear dissipation 


12.60.Jv 12.10.Dm 98.80.Cq 11.30.Hv 



U E Vincent is an alumnus of the Newton International Fellowships. He is supported by the Royal Society of London through their Newton International Fellowship Alumni Scheme.


  1. 1.
    P S Landa and P V E McClintock, J. Phys. A 33(45), L433 (2000)ADSGoogle Scholar
  2. 2.
    Y Ren, Y Pan, F Duan, F Chapeau-Blondeau and D Abbott, Phys. Rev. E 96, 022141 (2017)ADSGoogle Scholar
  3. 3.
    H G Liu, X L Liu, J H Yang, M A F Sanjuán and G Cheng, Nonlinear Dynam. 89(4), 2621 (2017)MathSciNetGoogle Scholar
  4. 4.
    M I Dykman, D G Luchinsky, R Mannella, P V E McClintock, N D Stein and N G Stocks, II Nuovo Cimento D 17(7–8), 661 (1995)ADSGoogle Scholar
  5. 5.
    J Casado-Pascual, J Gómez-Ordónez and M Morillo, Chaos 15(2), 26115 (2005)MathSciNetGoogle Scholar
  6. 6.
    S Zambrano, J M Casado and M A F Sanjuán, Phys. Lett. A 366, 428 (2007)ADSGoogle Scholar
  7. 7.
    A S Pikovsky and J Kurths, Phys. Rev. Lett. 78(5), 775 (1997)ADSMathSciNetGoogle Scholar
  8. 8.
    S Rajasekar and M A F Sanjuán, Nonlinear resonances, Springer series in synergetics (Springer, Switzerland, 2016)Google Scholar
  9. 9.
    S Rajamani, S Rajasekar and M A F Sanjuán, Commun. Nonlin. Sci. Numer. Simulat. 19(11), 4003 (2014)ADSGoogle Scholar
  10. 10.
    R Jothimurugan, K Thamilmaran, S Rajasekar and M A F Sanjuán, Nonlinear Dynam. 83(4),1803 (2016)MathSciNetGoogle Scholar
  11. 11.
    M Gitterman, J. Phys. A 34(24), L355 (2001)ADSMathSciNetGoogle Scholar
  12. 12.
    I I Blekhman and P S Landa, Int. J. Non-Linear Mech. 39(3), 421 (2004)ADSGoogle Scholar
  13. 13.
    S Rajasekar, K Abirami and M A F Sanjuán, Chaos 21(3), 033106 (2011)ADSMathSciNetGoogle Scholar
  14. 14.
    M Borromeo and F Marchesoni, Phys. Rev. E 73, 016142 (2006)ADSGoogle Scholar
  15. 15.
    C Jeevarathinam, S Rajasekar and M A F Sanjuán, arXiv:1504.04163v1 [nlin.CD] (2015)
  16. 16.
    S Jeyakumari, V Chinnathambi, S Rajasekar and M A F Sanjuán, Int. J. Bifurc. Chaos 21(1), 275 (2011)Google Scholar
  17. 17.
    Y Qin, J Wang, C Men, B Deng and X Wei, Chaos 21(2), 023133 (2011)ADSGoogle Scholar
  18. 18.
    H Yu, J Wang, C Liu, B Deng and X Wei, Chaos 21(4), 043101 (2011)ADSGoogle Scholar
  19. 19.
    X Wu, C Yao and J Shuai, Sci. Rep. 5, 7684 (2015)Google Scholar
  20. 20.
    Z Yang and L Ning, Pramana – J. Phys. 92(6): 89 (2019)ADSGoogle Scholar
  21. 21.
    J P Baltanás, L López, I I Blechman, P S Landa, A Zaikin, J Kurths and M A F Sanjuán, Phys. Rev. E 67, 066119 (2003)ADSGoogle Scholar
  22. 22.
    V N Chizhevsky, Phys. Rev. E 90, 042924 (2014)ADSGoogle Scholar
  23. 23.
    P R Venkatesh and A Venkatesan, Commun. Nonlin. Sci. Numer. Simulat. 39, 271 (2016)ADSGoogle Scholar
  24. 24.
    S Rajasekar, S Jeyakumari, V Chinnathambi and M A F Sanjuán, J. Phys. A 43(46), 465101 (2010)ADSMathSciNetGoogle Scholar
  25. 25.
    J H Yang, M A F Sanjuán, W Xiang and H Zhu, Pramana – J. Phys. 81(6), 943 (2013)ADSGoogle Scholar
  26. 26.
    B Deng, J Wang, X Wei, H Yu and H Li, Phys. Rev. E 89, 062916 (2014)ADSGoogle Scholar
  27. 27.
    C Jeevarathinam, S Rajasekar and M A F Sanjuán, Phys. Rev. E 83, 066205 (2011)ADSGoogle Scholar
  28. 28.
    J H Yang and X B Liu, Phys. Scr. 82(2), 025006 (2010)ADSGoogle Scholar
  29. 29.
    J H Yang and X B Liu, Chaos 20(3), 033124 (2010)ADSGoogle Scholar
  30. 30.
    J Yang and H Zhu, Chaos 22(1), 013112 (2012)ADSMathSciNetGoogle Scholar
  31. 31.
    J H Yang, M A F Sanjuán, F Tian and H F Yang, Int. J. Bifurc. Chaos 25(02), 1550023 (2015)Google Scholar
  32. 32.
    T L M Djomo Mbong, M S Siewe and C Tchawoua, Commun. Nonlin. Sci. Numer. Simulat. 22(1), 228 (2015)ADSGoogle Scholar
  33. 33.
    T O Roy-Layinde, J A Laoye, O O Popoola and U E Vincent, Chaos 26, 093117 (2016)ADSMathSciNetGoogle Scholar
  34. 34.
    T O Roy-Layinde, J A Laoye, O O Popoola, U E Vincent and P V E McClintock, Phys. Rev. E 96, 032209 (2017)ADSGoogle Scholar
  35. 35.
    U E Vincent, T O Roy-Layinde, O O Popoola, P O Adesina and P V E McClintock, Phys. Rev. E 98, 062203 (2018)ADSGoogle Scholar
  36. 36.
    Z Chen and L Ning, Pramana – J. Phys. 90: 49 (2018)ADSGoogle Scholar
  37. 37.
    S Jeyakumari, V Chinnathambi, S Rajasekar and M A F Sanjuán, Chaos 19(4), 043128 (2009)ADSGoogle Scholar
  38. 38.
    S Jeyakumari, V Chinnathambi, S Rajasekar and M A F Sanjuán, Phys. Rev. E 80, 046608 (2009)ADSGoogle Scholar
  39. 39.
    T L M D Mbong, M S Siewe and C Tchawoua, Mech. Res. Commun. 78, 13 (2016)Google Scholar
  40. 40.
    V N Chizhevsky, Phys. Rev E 89, 062914 (2014)ADSGoogle Scholar
  41. 41.
    C Jeevarathinam, S Rajasekar and M A F Sanjuán, Chaos 23(1), 013136 (2013)ADSMathSciNetGoogle Scholar
  42. 42.
    T Qin, T Xie, M Luo and K Deng, Chin. J. Phys. 55(2), 546 (2017)Google Scholar
  43. 43.
    P D’ancona and V  Pierfelice, J. Func. Anal. 227, 30 (2005)Google Scholar
  44. 44.
    F  Tantussi, D  Vella, M Allegrini, F Fuso, L Romoli and C A Rashed, Precis. Eng. 41, 32 (2015)Google Scholar
  45. 45.
    C Ma, Y Duan, B Yu, J Sun and Q Tu, J. Eng. Tribol. 23, 1307 (2017)Google Scholar
  46. 46.
    R Zwanzig, Proc. Natl. Acad. Sci. 85(7), 2029 (1988)ADSGoogle Scholar
  47. 47.
    S Banerjee, R Biswas, K Seki and B Bagchi, J. Chem. Phys. 141, 124105 (2014)ADSGoogle Scholar
  48. 48.
    M Volk, L Milanesi, J P Waltho, C A Huntere and G S Beddardf, Phys. Chem. Chem. Phys. 17(2), 762 (2015)Google Scholar
  49. 49.
    L  Milanesi, J P Waltho, C A Hunter, D J Shaw, G S Beddard, G D Reid, S Dev and M Volk, Proc. Natl. Acad. Sci. 109(48), 19563 (2012)ADSGoogle Scholar
  50. 50.
    Y Zhou, H Zhu, W Zhang, X Zuo, Y Li and J Yang, Adv. Mech. Eng. 7, 1 (2015)Google Scholar
  51. 51.
    A Y Wang, J L Mo, X C Wang, M H Zhu and Z R Zhou, Wear 402–403, 80 (2018)Google Scholar
  52. 52.
    Y Li, Y Xu and J Kurths, Phys. Rev. E 96, 052121 (2017)Google Scholar
  53. 53.
    D Mondal, P Ghosh and D Ray, J. Chem. Phys. 130(7), 074703 (2009)ADSGoogle Scholar
  54. 54.
    S Camargo and C Anteneodo, Physica A 495, 114 (2018)ADSMathSciNetGoogle Scholar
  55. 55.
    Y Li, Y Xu, J Kurths and X Yue, Chaos 27(10), 103102 (2017)ADSMathSciNetGoogle Scholar
  56. 56.
    Y Li, Y Xu, J Kurths and X Yue, Phys. Rev. E 94, 042222 (2016)ADSGoogle Scholar
  57. 57.
    K Abirami, S Rajasekar and M A F Sanjuán, Commun. Nonlin. Sci. Numer. Simulat. 47, 370 (2017)ADSGoogle Scholar
  58. 58.
    H G Enjieu Kadji, B R Nana Nbendjo, J B Chabi Orou and P K Talla, Phys. Plasmas 15(3), 032308 (2008)ADSGoogle Scholar
  59. 59.
    M S Siewe, H Cao and M A F Sanjuán, Chaos Solitons Fractals 41(2), 772 (2009)ADSGoogle Scholar
  60. 60.
    M S Siewe, M F M Kakmeni, C Tchawoua and P Woafo, Nonlinear response, and homoclinic chaos of driven charge density in plasma, Report 39090566 (International Atomic Energy Agency (IAEA), Abdus Salam International Centre for Theoretical Physics (Trieste, Italy, 2007))Google Scholar
  61. 61.
    J Dawson, Phys. Fluids 7(7), 981 (1964)ADSGoogle Scholar
  62. 62.
    H Okuda, Phys. Fluids 16(3), 408 (1973)ADSGoogle Scholar
  63. 63.
    S Gitomer, R Jones, F Begay, A Ehler, J Kephart and R Kristal, Phys. Fluids 29(8), 2679 (1986)ADSGoogle Scholar
  64. 64.
    F F Chen, Phys. Plasmas 2(6), 2164 (1995)ADSGoogle Scholar
  65. 65.
    A Bystrov and V Gildenburg, Plasma Phys. Rep. 27(1), 68 (2001)ADSGoogle Scholar
  66. 66.
    G Liu, T-C Chien, X Cao, O Lanes, E Alpern, D Pekker and M Hatridge, Appl. Phys. Lett. 111(20), 202603 (2017)ADSGoogle Scholar
  67. 67.
    S Boutin, D M Toyli, A V Venkatramani, A W Eddins, I Siddiqi and A Blais, Phys. Rev. Appl. 8, 054030 (2017)Google Scholar
  68. 68.
    D L Weerawarne, X Gao, A L Gaeta and B Shim, Phys. Rev. Lett. 114, 093901 (2015)ADSGoogle Scholar

Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  • J A Laoye
    • 1
  • T O Roy-Layinde
    • 1
    • 2
  • K A Omoteso
    • 1
  • O O Popoola
    • 1
  • U E Vincent
    • 3
    • 4
    Email author
  1. 1.Department of PhysicsOlabisi Onabanjo UniversityAgo-IwoyeNigeria
  2. 2.Department of PhysicsUniversity of IbadanIbadanNigeria
  3. 3.Department of Physical SciencesRedeemer’s UniversityEdeNigeria
  4. 4.Department of PhysicsLancaster UniversityLancasterUK

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