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When noise-free logical stochastic resonance occurs in a bistable system

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Abstract

An overdamped bistable system driven by a high-frequency periodic source and weak aperiodic logical inputs is investigated to find out that a sufficient condition for the emergence of noise-free logical stochastic resonance (NFLSR). By analyzing NFLSR in detailed, we proposed two essential features, the sign invariant and the initial value independent features, which can be regarded as a general principle to obtain potential logical systems. Applying the two features to the approximation solution of the overdamped bistable system, we obtained the sufficient conditions of the emergence of NFLSR, and the numerical simulations are in agreement with the analytical results. The sufficient conditions show us that a suitable periodic source can lead to the desired logic gate robustly near the pitchfork bifurcation point. This study can be used to complement the logical stochastic resonance response in the situation where noise is subthreshold, and besides, it also provides the principle and insights to effectively control or find out potential logical systems.

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References

  1. Benzi, R., Sutera, A., Vulpiani, A.: The mechanism of stochastic resonance. J. Phys. A Math. Gen. 14, L453 (1981)

    Article  MathSciNet  Google Scholar 

  2. Melnikov, V.I.: Schmitt trigger: a solvable model of stochastic resonance. Phys. Rev. E 48, 2481–2489 (1993)

    Article  Google Scholar 

  3. Gammaitoni, L., Hänggi, P., Jung, P., Marchesoni, F.: Stochastic resonance. Rev. Mod. Phys. 70, 223–287 (1998)

    Article  Google Scholar 

  4. Chen, H., Varshney, P.K., Kay, S.M., Michels, J.H.: Theory of the stochastic resonance effect in signal detection: part I-fixed detectors. IEEE Trans. Signal Process. 55, 3172–3184 (2007)

    Article  MathSciNet  Google Scholar 

  5. Chen, H., Varshney, P.K.: Theory of the stochastic resonance effect in signal detection-part II: variable detectors. IEEE Trans. Signal Process. 56, 5031–5041 (2008)

    Article  MathSciNet  Google Scholar 

  6. Murali, K., Rajamohamed, I., Sinha, S., Ditto, W.L., Bulsara, A.R.: Realization of reliable and flexible logic gates using noisy nonlinear circuits. Appl. Phys. Lett. 95, 194102 (2009)

  7. Murali, K., Sinha, S., Ditto, W.L., Bulsara, A.R.: Reliable logic circuit elements that exploit nonlinearity in the presence of a noise floor. Phys. Rev. Lett. 102, 104101 (2009)

    Article  Google Scholar 

  8. Bulsara, A.R., Dari, A., Ditto, W.L., Murali, K., Sinha, S.: Logical stochastic resonance. Chem. Phys. 375, 424–434 (2010)

    Article  Google Scholar 

  9. Zhang, L., Song, A., He, J.: Effect of colored noise on logical stochastic resonance in bistable dynamics. Phys. Rev. E 82, 051106 (2010)

    Article  Google Scholar 

  10. Dari, A., Kia, B., Bulsara, A.R., Ditto, W.: Creating morphable logic gates using logical stochastic resonance in an engineered gene network. Europhys. Lett. 93, 18001 (2011)

    Article  Google Scholar 

  11. Dari, A., Kia, B., Bulsara, A.R., Ditto, W.L.: Logical stochastic resonance with correlated internal and external noises in a synthetic biological logic block. Chaos 21, 047521 (2011)

    Article  MATH  Google Scholar 

  12. Kohar, V., Sinha, S.: Noise-assisted morphing of memory and logic function. Phys. Lett. A 376, 957–962 (2012)

    Article  MATH  Google Scholar 

  13. Sharma, A., Kohar, V., Shrimali, M.D., Sinha, S.: Realizing logic gates with time-delayed synthetic genetic networks. Nonlinear Dyn. 76, 431–439 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zhang, H., Yang, T., Xu, W., Xu, Y.: Effects of non-Gaussian noise on logical stochastic resonance in a triple-well potential system. Nonlinear Dyn. 76, 649–656 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  15. Wang, N., Song, A.: Parameter-induced logical stochastic resonance. Neurocomputing 155, 80–83 (2015)

    Article  Google Scholar 

  16. Gupta, A., Sohane, A., Kohar, V., Murali, K., Sinha, S.: Noise-free logical stochastic resonance. Phys. Rev. E 84, 055201 (2011)

    Article  Google Scholar 

  17. Kohar, V., Murali, K., Sinha, S.: Enhanced logical stochastic resonance under periodic forcing. Commun. Nonlinear Sci. Numer. Simul. 19, 2866–2873 (2014)

    Article  MathSciNet  Google Scholar 

  18. Venkatesh, P., Venkatesan, A.: Vibrational resonance and implementation of dynamic logic gate in a piecewise-linear Murali-Lakshmanan-Chua circuit. Commun. Nonlinear Sci. Numer. Simul. 39, 271–282 (2016)

    Article  MathSciNet  Google Scholar 

  19. Mano, M.M.: Computer system architecture. Prentice-Hall, Englewood, Cliffs, NJ (1993)

    MATH  Google Scholar 

  20. Cubero, D., Baltanás, J.P., Casado-Pascual, J.: High-frequency effects in the Fitzhugh-Nagumo neuron model. Phys. Rev. E 73, 061102 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  21. Chizhevsky, V.N., Giacomelli, G.: Improvement of signal-to-noise ratio in a bistable optical system: comparison between vibrational and stochastic resonance. Phys. Rev. A 71, 011801 (2005)

    Article  Google Scholar 

  22. Blekhman, I.I.: Vibrational mechanics. World Scientific, Singapore (2000)

    Book  MATH  Google Scholar 

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Acknowledgments

We would like to express our sincere appreciation and gratitude to the editors and reviewers for their help and constructive comments. The work was supported by the National Natural Science Foundation of China (Grant No. 11171238).

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu, 610065, Sichuan, China

    Bo Yang, Xiao Zhang & Mao-Kang Luo

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  1. Bo Yang
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  2. Xiao Zhang
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  3. Mao-Kang Luo
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Correspondence to Bo Yang.

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Yang, B., Zhang, X. & Luo, MK. When noise-free logical stochastic resonance occurs in a bistable system. Nonlinear Dyn 87, 1957–1965 (2017). https://doi.org/10.1007/s11071-016-3165-7

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  • DOI: https://doi.org/10.1007/s11071-016-3165-7

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