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The phenomenon of tristable stochastic resonance driven by \(\alpha \)-noise

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Abstract

In this paper, the tristable stochastic resonance (SR) phenomenon induced by \(\alpha \)-stable noise is analysed. The mechanism for realizing resonance is explored based on research concerning the potential function and resonant output of a system. The rules for resonance system parameters q, p, skewness parameter r and intensity amplification factor Q of \(\alpha \)-stable noise to act on the resonant output are explored under different values of stability index \(\alpha \) and asymmetric skewness \(\beta \) of \(\alpha \)-stable noise. The results will contribute to a reasonable selection of parameter-induced tristable SR system parameters under \(\alpha \)-stable noise, and lay the foundation for a practical engineering application of weak signal detection based on the SR.

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References

  1. B Ando and S Graziani, Stochastic resonance: Theory and applications (Kluwer Academic Publishers, 2000)

  2. S Rajasekar and M A F Sanjuan, Nonlinear resonances (Springer, 2016)

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

    Article  ADS  Google Scholar 

  4. J Fan, W L Zhao and M L Zhang, Acta Phys. Sin. 63, 110506 (2014), doi:10.7498/aps.63.110506

  5. C Nicolis, Tellus 34, 1 (2010), doi:10.1111/j.2153-3490.1982.tb01786.x

    ADS  MathSciNet  Google Scholar 

  6. Y C Hung and C K Hu, Comput. Phys. Commun. 182, 249 (2011), doi:10.1016/j.cpc.2010.07.002

    Article  ADS  Google Scholar 

  7. R Benzi, A Sutera and A Vulpiani, J. Phys. A: Math. Gen. 14, 453 (1981), doi:10.1088/0305-4470/14/11/006

    Article  ADS  Google Scholar 

  8. P M Shi, Q Li and D Y Han, 54, 526 (2016), doi:10.1016/j.cjph.2016.07.003

    Google Scholar 

  9. Y B Li, B L Zhang, Z X Liu and Z Y Zhang, Acta Phys. Sin. 63, 16054 (2014), doi:10.7498/aps.63.160504

    Google Scholar 

  10. Y Qin, Y Tao, Y He and B P Tang, J. Sound Vib. 333, 7386 (2014), doi:10.1016/j.jsv.2014.08.039

    Article  ADS  Google Scholar 

  11. J Wang and Q B He, IEEE Trans. Instrum. Meas. 64, 564 (2015), doi:10.1109/TIM.2014.2347217

    Article  Google Scholar 

  12. N G Stocks, N D Stein and P V E McClintock, J. Phys. A 26, 385 (1993), doi:10.1016/0375-9601(93)91186-9

  13. F Guo, H Li and L Jing, Chin. J. Phys. 53, 18 (2015), doi:10.6122/CJP.20141027A

    Google Scholar 

  14. I Gomes, C R Mirasso, R Toral and O Calvo, Physica A 327, 115 (2003), doi:10.1016/S0378-4371(03)00461-8

    Article  ADS  Google Scholar 

  15. C Masoller, Phys. Rev. Lett. 88, 034102 (2002), doi:10.1103/PhysRevLett.88.034102

    Article  ADS  Google Scholar 

  16. L Gammaitoni, F Marchesoni, E Menichella-Saetta and S Santucci, Phys. Rev. Lett. 62, 349 (1989), doi:10.1103/PhysRevLett.62.349

    Article  ADS  Google Scholar 

  17. Z Q Huang and F Guo, Chin. J. Phys. 54, 69 (2016), doi:10.1016/j.cjph.2016.03.005

    Article  Google Scholar 

  18. Z H Lai and Y G Leng, Sens. 15, 21327 (2015), doi:10.3390/s150921327

    Article  Google Scholar 

  19. Z H Lai and Y G Leng, Acta Phys. Sin. 64, 200502 (2015), doi:10.7498/aps.64.200503

    Google Scholar 

  20. S Arathi and S Rajasekar, Phys. Scr. 84, 065011 (2011), doi:10.1088/0031-8949/84/06/065011

    Article  ADS  Google Scholar 

  21. M P Shi, P Li and D Y Han, Acta Phys. Sin. 63, 170504 (2014), doi:10.7498/aps.63.170504

    Google Scholar 

  22. H Q Zhang, Y Xu, W Xu and X C Li, Chaos 22, 043130 (2012), doi:10.1063/1.4768729

    Article  ADS  MathSciNet  Google Scholar 

  23. H Q Zhang, T T Yang, W Xu and Y Xu, Nonlinear Dyn. 76, 649 (2014), doi:10.1007/s11071-013-1158-3

    Article  Google Scholar 

  24. G L Zhang, X L Lü and Y M Kang, Acta Phys. Sin. 61, 040501 (2012), doi:10.7498/aps.61.040501

    Google Scholar 

  25. S B Jiao, C Ren, P H Li, Q Zhang and G Xie, Acta Phys. Sin. 63, 070501 (2014), doi:10.7498/aps.63.070501

    Google Scholar 

  26. S B Jiao, C Ren, P H Li, Q Zhang and G Xie, Acta Phys. Sin. 64, 020502 (2015), doi:10.7498/aps.64.020502

    Google Scholar 

  27. G Zhang, T Hu and T Q Zhang, Acta Phys. Sin. 64, 220502 (2015), doi:10.7498/aps.64.220502

    Google Scholar 

  28. L Z Zeng and B H Xu, J. Phys. A 389, 5128 (2010), doi:10.1016/j.physa.2010.07.032

    Google Scholar 

  29. R Weron, Statist. Prob. Lett. 28, 165 (1996)

    Article  Google Scholar 

  30. Y J Liang and W Chen, Signal Process. 93, 242 (2013), doi:10.1016/j.sigpro.2012.07.035

    Article  Google Scholar 

  31. A Silchenko and C K Hu, Phys. Rev. E 63, 041105 (2001), doi:10.1103/PhysRevE.63.041105

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Institute of Information and Navigation, Air Force Engineering University, Xi’an, 710077, China

    Yulei Liu, Jun Liang, Nan Xiao & Zhenhao Zhang

  2. School of Automation and Information Engineering, Xi’an University of Technology, Xi’an, 710048, China

    Shang-Bin Jiao

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  1. Yulei Liu
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  2. Jun Liang
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  3. Shang-Bin Jiao
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  4. Nan Xiao
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  5. Zhenhao Zhang
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Correspondence to Yulei Liu.

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Liu, Y., Liang, J., Jiao, SB. et al. The phenomenon of tristable stochastic resonance driven by \(\alpha \)-noise. Pramana - J Phys 89, 73 (2017). https://doi.org/10.1007/s12043-017-1471-3

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  • DOI: https://doi.org/10.1007/s12043-017-1471-3

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