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Noise-free Set-Reset latch operation in nonlinear fractional-order systems

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Abstract

The Set-Reset latch is a fundamental part of computer systems and can be used to store information. However, the Set-Reset latch is only studied in integer-order systems, and real-world systems usually have memory effects. A fractional-order system will be more appropriate for a study. Therefore, this paper explores the impact of memory effects on the Set-Reset latch logic operation by studying the harmonic-driven Set-Reset latch operation in a nonlinear fractional-order two-well potential system. The results show that the system holds different memory effects at \(\alpha \in (\mathrm{0,1})\) and \(\alpha \in (\mathrm{1,2})\). However, the impact of memory effects can be eliminated under certain harmonic driving forces, so the system can form a stable logic gate and implement logical vibrational resonance (LVR). Finally, the relationship between LVR and the fractional order is studied. This research reveals the interesting dynamic properties of the fractional system and provides a reference for choosing a more practical system to implement LVR.

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References

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

    Article  ADS  Google Scholar 

  2. R.N. Mantegna, B. Spagnolo, Phys. Rev. E 49, R1792–R1795 (1994)

    Article  ADS  Google Scholar 

  3. J.M. Iannelli, A. Yariv, T.R. Chen, Y.H. Zhuang, Appl. Phys. Lett. 65, 1983–1985 (1994)

    Article  ADS  Google Scholar 

  4. J.E. Levin, J.P. Miller, Nature 380, 165–168 (1996)

    Article  ADS  Google Scholar 

  5. Y.C. Hung, C.K. Hu, Comput. Phys. Commun. 182, 249–250 (2011)

    Article  ADS  Google Scholar 

  6. G. Zhang, Y. Yang, T. Zhang, Chin. J. Phys. 60, 107–121 (2019)

    Article  Google Scholar 

  7. J. Xu, X. Luo, Chin. J. Phys. 63, 382–391 (2020)

    Article  Google Scholar 

  8. T.L. Carroll, L.M. Pecora, Phys. Rev. Lett. 70, 576–579 (1993)

    Article  ADS  Google Scholar 

  9. J. Ma, W.Y. Jin, Y.L. Li, Chaos Solitons Fractals 36, 494–499 (2008)

    Article  ADS  Google Scholar 

  10. S. Nobukawa, H. Nishimura, T. Yamanishi, J.Q. Liu, J. Artif. Intell. Soft Comput. Res. 5, 109–119 (2015)

    Article  Google Scholar 

  11. V. Baysal, Z. Sara, E. Yilmaz, Nonlinear Dyn. 97, 1275–1285 (2019)

    Article  Google Scholar 

  12. P.S. Landa, P.V.E. McClintock, J. Phys. A 33, L433 (2000)

    Article  ADS  Google Scholar 

  13. R. Feng, Y.Y. Zhao, C.P. Zhu, T.J. Mason, Ultrason. Sonochem. 9, 231–236 (2002)

    Article  Google Scholar 

  14. M. Ge, Y. Jia, Y. Xu, L. Yang, Nonlinear Dyn. 91, 515–523 (2017)

    Article  Google Scholar 

  15. L. Ning, Z. Chen, Physica D 401, 132164 (2020)

    Article  MathSciNet  Google Scholar 

  16. J.H. Yang, X.B. Liu, Chaos 20, 033124 (2010)

    Article  ADS  Google Scholar 

  17. L.J. Yang, W.H. Liu, M. Yi, C.J. Wang, Q.M. Zhu, X. Zhan, Y. Jia, Phys. Rev. E 86, 016209 (2012)

    Article  ADS  Google Scholar 

  18. L. Gammaitoni, Appl. Phys. Lett. 91, 224104 (2007)

    Article  ADS  Google Scholar 

  19. Y.G. Yao, J. Ma, R. Gui, G.H. Cheng, Chaos Solitons Fractals 152, 111339 (2021)

    Article  Google Scholar 

  20. Y.G. Yao, J. Ma, R. Gui, G.H. Cheng, Chaos 31, 023103 (2021)

    Article  ADS  Google Scholar 

  21. K. Murali, S. Sinha, W.L. Ditto, A.R. Bulsara, Phys. Rev. Lett. 102, 104–107 (2009)

    Article  Google Scholar 

  22. K.P. Singh, S. Sinha, Phys. Rev. E 83, 046219 (2011)

    Article  ADS  Google Scholar 

  23. D.N. Guerra, A.R. Bulsara, W.L. Ditto, S. Sinha, P. Mohanty, Nano Lett. 10, 1168–1171 (2010)

    Article  ADS  Google Scholar 

  24. M.A.A. Hafiz, L. Kosuru, M.I. Younis, J. Appl. Phys. 120, 074501 (2016)

    Article  ADS  Google Scholar 

  25. K. Murali, I. Rajamohamed, S. Sinha, W.L. Ditto, A.R. Bulsara, Appl. Phys. Lett. 95, 104101 (2009)

    Article  Google Scholar 

  26. L. Worschech, F. Hartmann, T.Y. Kim, S. Hoefling, M. Kamp, A. Forchel, J. Ahopelto, I. Neri, A. Dari, L. Gammaitoni, Appl. Phys. Lett. 96, 080503 (2010)

    Article  Google Scholar 

  27. P. Pfeffer, F. Hartmann, S. Höfling, M. Kamp, L. Worschech, Phys. Rev. Appl. 4, 014011 (2015)

    Article  ADS  Google Scholar 

  28. H. Ando, S. Sinha, R. Storni, K. Aihara, EPL 93, 50001 (2011)

    Article  ADS  Google Scholar 

  29. A. Dari, B. Kia, A.R. Bulsara, W. Ditto, EPL 93, 18001 (2011)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  31. S. Sinha, J.M. Cruz, T. Buhse, P. Parmananda, EPL 86, 60003 (2009)

    Article  ADS  Google Scholar 

  32. R. Storni, H. Ando, K. Aihara, K. Murali, S. Sinha, Phys. Lett. Sect. A. 376, 930–937 (2012)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  34. A. Gupta, A. Sohane, V. Kohar, K. Murali, S. Sinha, Phys. Rev. E 84, 055201 (2011)

    Article  ADS  Google Scholar 

  35. Y.G. Yao, J. Ma, Int. J. Bifurc. Chaos 30, 2050196 (2020)

    Article  Google Scholar 

  36. V. Kohar, K. Murali, S. Sinha, Commun. Nonlinear Sci. Numer. Simul. 19, 2866–2873 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  37. R. Gui, Y. Wang, Y.G. Yao, G.H. Cheng, Chaos Solitons Fractals 138, 109952 (2020)

    Article  Google Scholar 

  38. D. Cafagna, G. Grassi, Int. J. Bifurc. Chaos 16, 1521–1526 (2006)

    Article  Google Scholar 

  39. I. Campos-Cantón, E. Campos-Cantón, H.C. Rosu, E. Castellanos-Velasco, Circuits Syst. Signal Process. 31, 753–760 (2012)

    Article  Google Scholar 

  40. P.R. Venkatesh, A. Venkatesan, M. Lakshmanan, Chaos 27, 033105 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  41. V. Kohar, S. Sinha, Phys. Lett. Sect. A 376, 957–962 (2012)

    Article  ADS  Google Scholar 

  42. N. Wang, A. Song, Phys. Lett. Sect. A 378, 1588–1592 (2014)

    Article  Google Scholar 

  43. R. Gui, H.Y. Zhang, G.H. Cheng, Y.G. Yao, Chaos 30, 023119 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  44. R. Gui, Y.D. Yang, Y.G. Yao, G.H. Cheng, Chin. J. Phys. 68, 178–190 (2020)

    Article  Google Scholar 

  45. P.J. Torvik, R.L. Bagley, J. Appl. Mech. 51, 294–298 (1984)

    Article  ADS  Google Scholar 

  46. I. Podlubny, arXiv preprint, math/0110241 (2001)

  47. H. Sheng, Y.Q. Chen, T.S. Qiu, Fractional Processes and Fractional-Order Signal Processing: Techniques and Applications (Springer, London, 2011)

    MATH  Google Scholar 

  48. K. Assaleh, W.M. Ahmad, Modeling of speech signals using fractional calculus, in 2007 9th International Symposium on Signal Processing and Its Applications (IEEE, Sharjah, 2007), pp. 1–4

  49. C. Telke, M. Beitelschmidt, PAMM 15, 671–672 (2015)

    Article  Google Scholar 

  50. V.V. Kulish, J.L. Lage, J. Fluids Eng. 124, 803–806 (2002)

    Article  Google Scholar 

  51. M.A.A. Da Silva, G.M. Viswanathan, J.C. Cressoni, Physica D 421, 522–532 (2015)

    Article  Google Scholar 

  52. V. Zaburdaev, S. Denisov, J. Klafter, Rev. Mod. Phys. 87, 483–530 (2015)

    Article  ADS  Google Scholar 

  53. S.B. Yuste, E. Abad, K. Lindenberg, Phys. Rev. E 82, 061123 (2010)

    Article  ADS  Google Scholar 

  54. I.M. Sokolov, M.G.W. Schmidt, F. Sagués, Phys. Rev. E 73, 031102 (2006)

    Article  ADS  Google Scholar 

  55. M.J. Hou, J.H. Yang, S. Shi, H.G. Liu, Eur. Phys. J. Plus 135, 747 (2020)

    Article  Google Scholar 

  56. C.X. Zhu, Y. Zou, Control Decis. 24, 161–169 (2009)

    MathSciNet  Google Scholar 

  57. Z.Z. Sun, X.N. Wu, Appl. Numer. Math. 56, 193–209 (2006)

    Article  MathSciNet  Google Scholar 

  58. G.C. Wu, M.K. Luo, L.L. Huang, S. Banerjee, Nonlinear Dyn. 100, 3611–3623 (2020)

    Article  Google Scholar 

  59. L.L. Huang, J.H. Park, G.C. Wu, Z.W. Mo, J. Comput. Appl. Math. 370, 112633 (2020)

    Article  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. School of Mathematics and Physics, China University of Geosciences, Wuhan, 430074, China

    Qian Cheng, Min Li, Zhouchao Wei & Ming Yi

  2. Department of Physics, College of Science, Huazhong Agricultural University, Wuhan, 430070, China

    Yuangen Yao

Authors
  1. Qian Cheng
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  2. Yuangen Yao
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  3. Min Li
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Correspondence to Ming Yi.

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Cheng, Q., Yao, Y., Li, M. et al. Noise-free Set-Reset latch operation in nonlinear fractional-order systems. Eur. Phys. J. Plus 137, 948 (2022). https://doi.org/10.1140/epjp/s13360-022-03197-2

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