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Logical stochastic resonance in bistable system under α-stable noise

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Abstract

In the presence of α-stable noise, the logical stochastic resonance (LSR) phenomenon in a class of double well nonlinear system is investigated in this paper. LSR effect is obtained under α-stable noise. The probability of getting correct logic outputs is used to evaluate LSR behavior. Four main results are presented. Firstly, in the optimal band of noise intensity, Gaussian white noise is considered a better choice than heavy tailed noise to obtain clean logic operation. But at weak noise background, the success probability of getting the right logic outputs is higher when the system is subjected to heavy tailed noise. Secondly, it is shown that over the entire range of noise variance, the asymmetric noise induced LSR performs better than that induced by the symmetric noise. Furthermore, we find which side the tail skews also affects the correct probability of LSR. At last, the fractional Fokker-Planck equation is presented to show when the characteristic exponent of α-stable noise is less than 1, LSR behavior will not be obtained irrespective of the setting for other parameters.

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References

  1. R. Benzi, A. Satura, A. Vulpiani, J. Phys. A 14, L453 (1981)

    Article  ADS  Google Scholar 

  2. R. Benzi, G. Parisi, A. Sutera, Tellus 34, 10 (1982)

    Article  ADS  Google Scholar 

  3. R. Benzi, G. Parisi, A. Sutera, SIAM J. Appl. Math. 43, 565 (1983)

    Article  MathSciNet  Google Scholar 

  4. P. Hänggi, ChemPhysChem 3, 285 (2002)

    Article  Google Scholar 

  5. L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, Rev. Mod. Phys. 70, 223 (1998)

    Article  ADS  Google Scholar 

  6. K. Murali, S. Sinha, W.L. Ditto, A.R. Bulsara, Phys. Rev. Lett. 102, 104101 (2009)

    Article  ADS  Google Scholar 

  7. K. Murali, I. Rajamohamed, S. Sinha, W. Ditto, A.R. Bulsara, Appl. Phys. Lett. 95, 194102 (2009)

    Article  ADS  Google Scholar 

  8. G. Animesh, S. Aman, K. Vivek, K. Murali, S. Sudeshna, Phys. Rev. E 84, 055201 (2011)

    Article  Google Scholar 

  9. S. Remo, A. Hiroyasu, A. Kazuyuki, K. Muruli, S. Sudeshna, Phys. Lett. A 376, 930 (2012)

    Article  Google Scholar 

  10. V. Kohar, S. Sinha, Phys. Lett. A 376, 957 (2012)

    Article  ADS  MATH  Google Scholar 

  11. A. Dari, B. Kia, A.R. Bulsara, W. Ditto, Europhys. Lett. 93, 18001 (2011)

    Article  ADS  Google Scholar 

  12. A. Dari, B. Kia, X. Wang, A.R. Bulsara, W. Ditto, Phys. Rev. E 83, 041909 (2011)

    Article  ADS  Google Scholar 

  13. E.H. Hellen, S.K. Dana, J. Kurths, E. Kehler, S. Sinha, PLoS ONE 8, e76032 (2013)

    Article  ADS  Google Scholar 

  14. H. Zhang, Y. Xu, W. Xu, X. Li, Chaos 22, 043130 (2012)

    Article  ADS  Google Scholar 

  15. L. Zhang, A.G. Song, J. He, Phys. Rev. E 82, 051106 (2010)

    Article  ADS  Google Scholar 

  16. L. Zhang, A.G. Song, J. He, Eur. Phys. J. B 80, 147 (2011)

    Article  ADS  Google Scholar 

  17. M. Das, D.S. Ray, Phys. Rev. E 88, 032122 (2013)

    Article  ADS  Google Scholar 

  18. L. Zeng, J. Li, J. Shi, Chaos Solitons Fractals 45, 378 (2012)

    Article  ADS  Google Scholar 

  19. T. Srokowski, Eur. Phys. J. B 85, 65 (2012)

    Article  ADS  Google Scholar 

  20. J. Huang, W. Tao, B. Xu, Chin. Phys. Lett. 29, 010501 (2012)

    Article  ADS  Google Scholar 

  21. B. Dybiec, E. Gudowska-Nowak, Acta Phys. Pol. B 37, 1479 (2006)

    ADS  Google Scholar 

  22. B. Dybiec, E. Gudowska-Nowak, J. Stat. Mech. 2009, P05004 (2009)

    Google Scholar 

  23. K. Szczepaniec, B. Dybiec, Eur. Phys. J. B 86, 468 (2013)

    Article  ADS  Google Scholar 

  24. Y. Tang, W. Zou, J. Lu, J. Kurths, Phys. Rev. E 85, 046207 (2012)

    Article  ADS  Google Scholar 

  25. Y. Xu, J. Li, J. Feng, H. Zhang, W. Xu, J. Duan, Eur. Phys. J. B 86, 198 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  26. A. Janicki, A. Weron, Simulation and Chaotic Behavior of α Stable Stochastic Processes (Marcel Dekker, New York, 1994)

  27. H.C. Fogedby, Phys. Rev. Lett. 73, 2517 (1994)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. School of Instrument Science and Engineering, Southeast University, Sipailou 2, Nanjing, 210096, P.R. China

    Nan Wang & Aiguo Song

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  1. Nan Wang
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  2. Aiguo Song
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Correspondence to Aiguo Song.

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Wang, N., Song, A. Logical stochastic resonance in bistable system under α-stable noise. Eur. Phys. J. B 87, 117 (2014). https://doi.org/10.1140/epjb/e2014-50193-2

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  • DOI: https://doi.org/10.1140/epjb/e2014-50193-2

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