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Stochastic resonance induced by Gaussian white noise and Lévy noise in simplified FitzHugh–Nagumo neural system

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Abstract

This paper aims to investigate the stochastic resonance (SR) of simplified FitzHugh–Nagumo (FHN) neuron system driven by Gaussian white noise and Lévy noise. The Lévy noise is generated by Janicki–Weron algorithm, and the numerical solutions of system equation are obtained by the fourth-order stochastic Runge–Kutta algorithm. Then, the SR is determined by the classical measure of signal-to-noise ratio (SNR). Finally, the effects of the Gaussian white noise, Lévy noise and system parameters on SNR are discussed by means of numerical simulation. The results show that the larger stability index and skewness parameter are conducive to enhance signal response of FHN neural system; on the contrary, the increase in amplitude \( A \) and system parameter \( \gamma \) weakens the occurrence of SR.

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References

  1. W Horsthemke and R Lefever Noise-Induced Transitions: Theory and Applications in Physics, Chemistry and Biology (Berlin: Springer) Chapter 6, p 108 (1984)

  2. C W Gardiner Handbook of Stochastic Methods, 2nd ed.(Berlin: Springer) Chapter 9, p 342 (1985)

  3. R Benzi, G Parisi, A Sutera and A Vulpiani Tellus 34 10 (1982)

    ADS  Google Scholar 

  4. R Benzi, G Parisi, A Sutera and A Vulpiani Siam J. Appl. Math 43 565 (1983)

    Google Scholar 

  5. B McNamara and K Wiesenfeld Phys. Rev. A 39 4854 (1989)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  7. S Fauve and F Heslot Phys. Lett. A 97 5(1983)

    ADS  Google Scholar 

  8. M I Dykman, R Mannella, P V E McClintock and N G Stocks Phys. Rev. A 42 7041 (1990)

    ADS  Google Scholar 

  9. G Hu, G Nicolis and C Nicolis Phys. Rev. A 42 2030 (1990)

    ADS  Google Scholar 

  10. T Zhou and F Moss Phys. Rev. A 41 4255 (1990)

    ADS  Google Scholar 

  11. Y Xu, R C Gu, H Q Zhang, W Xu and J Q Duan Phys. Rev. E 83 056215 (2011)

    ADS  Google Scholar 

  12. Y C Hung and C K Hu Comput. Phys. Commun 182 249 (2011)

    ADS  Google Scholar 

  13. Y Jia, S N Yu and J R Li Phys. Rev. E 62 1869 (2000)

    ADS  Google Scholar 

  14. X L Li and L J Ning Indian J. Phys 90 91 (2016)

    ADS  Google Scholar 

  15. N V Agudov, A V Krichigin, D Valenti and B Spagnolo Phys. Rev. E 81 051123 (2010)

    ADS  Google Scholar 

  16. D Valenti, A Fiasconaro and B Spagnolo Acta Phys. Pol. B 35 1481 (2004)

    ADS  Google Scholar 

  17. A L Barbera and B Spagnolo Phys. A 314 120 (2002)

    MathSciNet  Google Scholar 

  18. A Fiasconaro, D Valenti and B Spagnolo Acta Phys. Pol. B 35 1491 (2004)

    ADS  Google Scholar 

  19. R N Mantegna and B Spagnolo Phys. Rev. E 49 R1792 (1994)

    ADS  Google Scholar 

  20. N V Agudov, A A Dubkov and B Spagnolo Phys. A 325 144 (2003)

    MathSciNet  Google Scholar 

  21. D Valenti, L Magazzù, P Caldara and B Spagnolo Phys. Rev. B 91 235412 (2015)

    ADS  Google Scholar 

  22. B Spagnolo, C Guarcello, L Magazzù and A Carollo Entropy 19 20 (2017)

    ADS  Google Scholar 

  23. M A Fuentes, R Toral and H S Wio Phys. A 295 114 (2001)

    Google Scholar 

  24. M A Fuentes, H S Wio and R Toral Phys. A 303 91 (2002)

    MathSciNet  Google Scholar 

  25. B C Bag, K G Petrosyan and C K Hu Phys. Rev. E 76 056210 (2007)

    ADS  Google Scholar 

  26. Y M Kang, X Chen, X D Lin and N Tan Fluct. Noise. Lett. 16 175007 (2017)

    Google Scholar 

  27. A A Dubkov and B Spagnolo Eur. Phys. J. B 65 361 (2008)

    ADS  MathSciNet  Google Scholar 

  28. D Valenti, C Guarcello and B Spagnolo Phys. Rev. B 89 214510 (2014)

    ADS  Google Scholar 

  29. A Janicki and A Weron Simulation and Chaotic Behavior of α-Stable Stochastic Processes (New York: Marcel Dekker) Chapter 3, p 35 (1994)

  30. A Weron and R Weron Computer Simulation of Lévy α-Stable Variables and Processes (Berlin: Springer) p 380 (1995)

    MATH  Google Scholar 

  31. R Weron (1996) Stat. Probab. Lett. 28 165

    Google Scholar 

  32. B Dybiec and E Gudowska-Nowak Acta Phys. Pol. B 37 1479 (2006)

    ADS  Google Scholar 

  33. B Dybiec and E Gudowska-Nowak J. Stat. Mech. Theory Exp. 5 P05004 (2009)

    Google Scholar 

  34. A La Cognata, D Valenti, A A Dubkov and B Spagnolo Phys. Rev. E 82 011121 (2010)

    ADS  Google Scholar 

  35. G Augello, D Valenti and B Spagnolo Eur. Phys. J. B 78 225 (2010)

    ADS  Google Scholar 

  36. A A Dubkov, B Spagnolo and V V Uchaikin Int. J. Bifurc. Chaos 18 2649 (2008)

    Google Scholar 

  37. L Zeng and B Xu Phys. A 389 5128 (2010)

    Google Scholar 

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

    ADS  Google Scholar 

  39. Y Xu, J Wu, L Du and H Yang Chaos Soliton Fractals 92 91 (2016)

    ADS  Google Scholar 

  40. W Xu, M L Hao, X D Gu and G D Yang Mod. Phys. Lett. B 28 1450085 (2014)

    ADS  Google Scholar 

  41. A L Hodgkin and A F Huxley Physiology 117 500 (1952)

    Google Scholar 

  42. R Fitzhhugh J. Gen. Physiol. 43 867 (1960)

    Google Scholar 

  43. T Alarcon, A Perez-Madrid and J M Rubi Phys. Rev. E 57 4979 (1998)

    ADS  Google Scholar 

  44. D Fan and L Hong Commun. Nonlinear Sci. Numer. Simul. 15 1873 (2010)

    ADS  MathSciNet  Google Scholar 

  45. D Tatchim Bemmo, M Siewe Siewe and C Tchawoua Commun. Nonlinear Sci. Numer. Simul. 18 1275 (2013)

    ADS  MathSciNet  Google Scholar 

  46. Z Q Wang, Y Xu and H Yang Sci. China Technol. Sci. 59 371 (2016)

    ADS  Google Scholar 

  47. Y G Yao, C Z Ma, C J Wang, M Yi and R Gui Phys. A 492 1247 (2018)

    MathSciNet  Google Scholar 

  48. Y G Yao and J Ma Cognit. Neurodyn. 12 343 (2018)

    Google Scholar 

  49. D Valenti, G Augello and B Spagnolo Eur. Phys. J. B 65 443 (2008)

    ADS  MathSciNet  Google Scholar 

  50. E V Pankratova, A V Polovinkin and B Spagnolo Phys. Lett. A 344 43 (2005)

    ADS  Google Scholar 

  51. Y F Guo, B Xi, F Wei and J G Tan Int. J. Mod. Phys. B 31 1750264 (2017)

    ADS  Google Scholar 

  52. L H Rebecca Phys. Rev. A 45 600 (1992)

    Google Scholar 

  53. L H Rebecca Phys. Rev. A 45 604 (1992)

    Google Scholar 

  54. S Mitaim and B Kosko Proc. IEEE 86 2152 (1998)

    Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 11672207) and the Tianjin Natural Science Foundation of China (Grant Nos. 17JCYBJC15700 and 17JCQNJC03800).

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Authors and Affiliations

  1. School of Mathematical Sciences, Tianjin Polytechnic University, Tianjin, 300387, People’s Republic of China

    Yongfeng Guo, Linjie Wang, Fang Wei & Jianguo Tan

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  1. Yongfeng Guo
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  2. Linjie Wang
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  3. Fang Wei
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  4. Jianguo Tan
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Correspondence to Yongfeng Guo.

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Guo, Y., Wang, L., Wei, F. et al. Stochastic resonance induced by Gaussian white noise and Lévy noise in simplified FitzHugh–Nagumo neural system. Indian J Phys 94, 1625–1632 (2020). https://doi.org/10.1007/s12648-019-01606-4

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  • DOI: https://doi.org/10.1007/s12648-019-01606-4

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