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Stochastic resonance and free oscillation in a sinusoidal potentials driven by a square-wave periodic force

  • Regular Article - Statistical and Nonlinear Physics
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Abstract

Recently, the occurrence of stochastic resonance in a sinusoidal potential driven by a sinusoidal force and a Gaussian white noise was experimentally verified. In this work, we experimentally show that stochastic resonance in sinusoidal potentials can also be observed when driven by a square-wave periodic force. The occurrence of stochastic resonance could be explained as due to the appearance of two dynamical states similar to what was done when driven by a sinusoidal force at large frequencies. However, at smaller frequencies of the square-wave drive, the free but damped oscillations of the output could be observed and the effective exponential damping coefficients measured.

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Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: The data can be made available from the authors if asked for.]

References

  1. S. Fauve, F. Heslot, Phys. Lett. A 97A, 5 (1983)

    Article  ADS  Google Scholar 

  2. B. McNamara, K. Wiesenfeld, R. Roy, Phys. Rev. Lett. 60, 2626 (1988)

    Article  ADS  Google Scholar 

  3. R. Benzi, A. Sutera, A. Vulpiani, J. Phys. A Math. Gen. 14, L453 (1981)

    Article  ADS  Google Scholar 

  4. R. Benzi, G. Parisi, A. Sutera, A. Vulpiani, Stochastic resonance in climatic change. Tellus 34, 10–16 (1982)

    Article  ADS  MATH  Google Scholar 

  5. C. Nicolis, Tellus 34, 1 (1982)

    Article  ADS  MathSciNet  Google Scholar 

  6. A.R. Bulsara, L. Gammaitoni, Tuning in to noise. Phys Today (1996)

  7. M.I. Dykmann et al., Stochastic resonance in perspective. Il Nuovo Cimento 17D, 7–8 (1995)

    Google Scholar 

  8. F. Chapeau-Blondeau, Noise-enhanced capacity via stochastic resonance in an asymmetric binary channel. Phys. Rev. E 55, 2 (1997)

    Article  Google Scholar 

  9. V. Bedichevsky, M. Gitterman, Stochastic resonance in a bistable piecewise potential: analytical solution. J. Phys. A Math. Gen. 29, L447 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  10. P. Jung, P. H\(\ddot{a}\)nggi, “Amplification of small signals via stochastic resonance,” Phys. Rev. A, vol. 44, p. 12, (1991)

  11. L. Gammaitoni, F. Marchesoni, E. Menichella-Saetta, S. Santucci, Stochastic resonance in bistable system. Phys. Rev. Lett. 62, 4 (1989)

    Article  MATH  Google Scholar 

  12. L. Gammaitoni, Stochastic resonance and the dithering effect in threshold physical systems. Phys. Rev. E 52, 5 (1995)

    Article  Google Scholar 

  13. L. Gammaitoni, P. Hanggi, P. Jung, F. Marchesoni, Stochastic resonance. Rev. Mod. Phys. 70, 1 (1998)

    Article  Google Scholar 

  14. S.M. Bezrukov, I. Vodyanoy, Stochastic resonance in nondynamical systems without response thresholds. Nature 385, 319–321 (1997)

    Article  ADS  Google Scholar 

  15. F. Chapeau-Blondeau, X. Godovier, Theory of stochastic resonance in signal transmission by static nonlinear systems. Phys. Rev. E 55, 2 (1997)

    Article  Google Scholar 

  16. A. S. Asdi, A. H. Tewfik, Detection of weak signals using adaptive stochastic resonance. In: IEEE International Conference on Acoustic, Speech, Signal Processing, vol. 2 (1995)

  17. B. McNamara, K. Wiesenfeld, Phys. Rev. A 39, 4854 (1989)

    Article  ADS  Google Scholar 

  18. J.K. Douglass, L. Wilkens, E. Pantazelou, F. Moss, Nature (London) 365, 337 (1993)

    Article  ADS  Google Scholar 

  19. K. Wiesenfeld, F. Moss, Nature (London) 373, 33 (1995)

    Article  ADS  Google Scholar 

  20. H. Chen, P. Varshney, S. Kay, J. Michels, Theory of the stochastic resonance effect in signal detection: Part I-Fixed detectors. IEEE Trans. Signal Process. 55(7), 3172–3184 (2007)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  21. H. Chen, P. Varshney, Theory of the stochastic resonance effect in signal detection-Part ii: variable detectors. IEEE Trans. Signal Process. 56(10), 5031–5041 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. S. Zozor, P.-O. Amblard, Stochastic resonance in locally optimal detectors. IEEE Trans. Signal Process. 51(12), 3177–3181 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  23. D.G. Luchinsky, R. Mannella, P.V.E. McClintock, N.G. Stocks, Stochastic resonance in electrical circuits-Part I: conventional stochastic resonance. IEEE Trans. Circuits Syst. II Analog Digit. Signal Process. 46(9), 1205–1214 (1999)

    Article  Google Scholar 

  24. D.G. Luchinsky, R. Mannella, P.V.E. McClintock, N.G. Stocks, Stochastic resonance in electrical circuits-Part II: nonconventional stochastic resonance. IEEE Trans. Circuits Syst. II Analog Digit. Signal Process. 46(9), 1215–1224 (1999)

    Article  Google Scholar 

  25. M. McDonnell, Is electrical noise useful? [Point of view]. Proc. IEEE 99(2), 242–246 (2011)

    Article  Google Scholar 

  26. G. Harmer, B. Davis, D. Abbott, A review of stochastic resonance: circuits and measurement. IEEE Trans. Instrum. Meas. 51(2), 299–309 (2002)

    Article  Google Scholar 

  27. D.S. Leonard, L. Reichl, Stochastic resonance in a chemical reaction. Phys. Rev. E 49(2), 1734–1737 (1994)

    Article  ADS  Google Scholar 

  28. H.S. Wio, Phys. Rev. E 54, R3075 (1996)

    Article  ADS  MathSciNet  Google Scholar 

  29. H.S. Wio, J.A. Revelli, M.A. Rodriguez, R.R. Deza, G.G. Izús, Eur. Phys. J. B 69, 71–80 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  30. L. Gammaitoni, P. Hanggi, P. Jung, F. Marchesoni, Eur. Phys. J. B 69, 1–3 (2009)

    Article  ADS  Google Scholar 

  31. L. Gammaitoni, P. Hanggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 223–287 (1998). (For an early review see )

    Article  ADS  Google Scholar 

  32. V.I. Melnikov, Schmitt trigger: a solvable model of stochastic resonance. Phys. Rev. E 48, 4 (1993)

    Article  Google Scholar 

  33. M.I. Dykman, D.G. Luchinsky, R. Mannella, P.V.E. McClintock, N.D. Stein, N.G. Stocks, JETP Lett. 58, 150 (1993)

    ADS  Google Scholar 

  34. M.I. Dykman, D.G. Luchinsky, R. Mannella, P.V.E. McClintock, N.D. Stein, N.G. Stocks, Phys. Rev. E 49, 1198 (1994)

    Article  ADS  Google Scholar 

  35. N.G. Stocks, N.D. Stein, S.M. Soskin, P.V.E. McClintock, J. Phys. A Math. Gen. 25, L1119 (1992)

    Article  ADS  Google Scholar 

  36. N.G. Stocks, N.D. Stein, P.V.E. McClintock, J. Phys. A Math. Gen. 26, L385 (1993)

    Article  ADS  Google Scholar 

  37. S. Saikia, A.M. Jayannavar, M.C. Mahato, Phys. Rev. E 83, 1 (2011)

    Article  Google Scholar 

  38. W.L. Reenbohn, S.S. Pohlong, M.C. Mahato, Phys. Rev. E 85, 1 (2012)

    Article  Google Scholar 

  39. W.L. Reenbohn, M.C. Mahato, Phys. Rev. E 88, 1 (2013)

    Article  Google Scholar 

  40. W.L. Reenbohn, M.C. Mahato, Phys. Rev. E 91, 1 (2015)

    Article  Google Scholar 

  41. D. Kharkongor, W.L. Reenbohn, M.C. Mahato, Phys. Rev. E 94, 1 (2016)

  42. T. Iwai, Phys. A 300, 350 (2001)

    Article  Google Scholar 

  43. M. Evstigneev, P. Reimann, C. Schmitt, C. Bechinger, J. Phys. Condens. Matter 17, S3795 (2005)

    Article  ADS  Google Scholar 

  44. M.C. Mahato, S.R. Shenoy, Phys. Rev. E 50, 2503 (1994)

    Article  ADS  Google Scholar 

  45. K. Sekimoto, J. Phys. Soc. Jpn. 66, 1234 (1997)

    Article  ADS  Google Scholar 

  46. R.-N. Liu, Y.-M. Kang, Phys. Lett. A 382, 1656 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  47. P.V.E. McClintock, F. Moss, Noise in Nonlinear Dynamical Systems, ed. by F. Moss and P.V.E. McClintock, vol. 3 (Cambridge University Press, Cambridge, 1989), p. 243

    Book  Google Scholar 

  48. D.G. Luchinsky, R. Mannella, P.V.E. McClintock, N.G. Stocks, IEEE Trans. Circuits Syst. II Analog Digit. Signal Process. 46, 1215 (1999)

    Article  Google Scholar 

  49. E.A. Desloge, Am. J. Phys. 62, 601 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  50. I.S. Sawkmie, M.C. Mahato, Commun. Nonlinear Sci. Numer. Simulat. 78, 104859 (2019)

    Article  Google Scholar 

  51. K. Johannessen, An analytical solution to the equation of motion for the damped nonlinear pendulum. Eur. J. Phys. 35, 035014 (2014)

    Article  MATH  Google Scholar 

  52. J.A. Blackburn, S. Vik, B. Wu, Driven pendulum for studying chaos. Rev. Sci. Instrum. 50, 3 (1989)

    Google Scholar 

  53. J.A. Blackburn, G.L. Baker, A comparison of commercial chaotic pendulums. Am. J. Phys. 66, 9 (1998)

    Article  Google Scholar 

  54. P.T. Squire, Pendulum damping. Am. J. Phys. 54, 984 (1986)

    Article  ADS  Google Scholar 

  55. I.S. Sawkmie, M.C. Mahato, Phys. Educ. 1(4), 1950015 (2019)

    Article  Google Scholar 

  56. Ivan S. Sawkmie, M.C. Mahato, An analog simulation experiment to study free oscillations of a damped simple pendulum, arXiv:1903.06162 [physics.class-ph]

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Authors and Affiliations

  1. Department of Physics, North-Eastern Hill University, Shillong, 793022, India

    Ivan Skhem Sawkmie & Mangal C. Mahato

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  1. Ivan Skhem Sawkmie
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Correspondence to Mangal C. Mahato.

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Sawkmie, I.S., Mahato, M.C. Stochastic resonance and free oscillation in a sinusoidal potentials driven by a square-wave periodic force. Eur. Phys. J. B 94, 44 (2021). https://doi.org/10.1140/epjb/s10051-020-00011-9

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  • DOI: https://doi.org/10.1140/epjb/s10051-020-00011-9

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