Stochastic resonance in a monostable system driven by time-delayed feedback

  • Gang Zhang
  • Lin ZhouEmail author
  • Tianqi Zhang
Original Paper


The characteristic of a monostable stochastic resonance system driven by time-delayed feedback is investigated. Under the small-delay approximation theory, the effective potential function of the system is obtained and the influence of system parameters on the shape of the potential function is also discussed. Furthermore, we consider the influence of the input signal on the system and derive the asymmetric bistable potential function. By using the adiabatic approximation theory and the two-state theory, the theoretical expressions of the steady-state probability distribution function, mean first-passage time and signal-to-noise ratio are obtained, which are three excellent metrics to measure the performance of system. Simulation results show that the parameters A, a and τ can motivate the SR phenomenon while β suppresses the SR phenomenon. At last, the numerical simulation results obtained from the original Langevin equation and the effective Langevin equation can verify whether the theoretical derivation is correct.


Stochastic resonance Time-delayed feedback Classical monostable system 


05.40.-a 02.50.-r 



This work was supported by the National Natural Science Foundation of China (Nos. 61771085, 61671095, 61371164) and the Project of Key Laboratory of Signal and Information Processing of Chongqing (No. CSTC2009CA2003).


  1. [1]
    N Yeung, M M Botvinick and J D Cohen Psychol Rev. 111 931 (2004)CrossRefGoogle Scholar
  2. [2]
    B M Grafov and I B Grafova Electrochem Commun. 2 386 (2000)CrossRefGoogle Scholar
  3. [3]
    M Blanco-Velasco, B Weng and K E Barner Comput Biol Med. 38 1 (2008)CrossRefGoogle Scholar
  4. [4]
    Y S Fan and G T Zheng Mech Syst Signal Pr.21 678 (2013)CrossRefGoogle Scholar
  5. [5]
    V N Hari, G V Anand and A B Premkumar Digit Signal Process. 23 1645 (2013)MathSciNetCrossRefGoogle Scholar
  6. [6]
    K Wiesenfeld, D Pierson, E Pantazelou and C Dames Phys Rev Lett.72 2125 (1994)ADSCrossRefGoogle Scholar
  7. [7]
    C Z Feng and W L Duan Indian J. Phys.88 107 (2014)ADSCrossRefGoogle Scholar
  8. [8]
    M Sahoo and A M Jayannavar Indian J. Phys.84 1421(2010)ADSCrossRefGoogle Scholar
  9. [9]
    P W Miller, L W McGowan, U Bergmann and D Farrell Med Hypotheses. 121 106(2018)CrossRefGoogle Scholar
  10. [10]
    V Ravichandran, V Chinnathambi and S Rajasekar Indian J. Phys.83 1593 (2009)Google Scholar
  11. [11]
    S L Lu, Q B He and J Wang Mech Syst Signal Pr. 116 230 (2019)CrossRefGoogle Scholar
  12. [12]
    S L Lu, Q B He and J W Zhao Mech Syst Signal Pr. 113 36 (2018)CrossRefGoogle Scholar
  13. [13]
    P Zandiyeh, J C Kupper, N G H Mohtadi and P Goldsmith G Biomech. 84 52(2019)Google Scholar
  14. [14]
    O White, J Babic, C Trenado and L Johannsen Front Physiol. 9 1865(2019)CrossRefGoogle Scholar
  15. [15]
    S L Lu, R Q Yan and Y B Liu IEEE T Instrum Meas. 28 2135(2019)Google Scholar
  16. [16]
    N V Agudov, A V Krichigin, D Valenti and B Spagnolo Phys Rev E. 81 051123 (2010)ADSCrossRefGoogle Scholar
  17. [17]
    R Y Chen and L R Nie Indian J. Phys.91 973 (2017)ADSCrossRefGoogle Scholar
  18. [18]
    H Q Zhang, Y Xu, W Xu and X C Li Chaos. 22 043130 (2012)ADSMathSciNetCrossRefGoogle Scholar
  19. [19]
    D C Mei, G Z Xie, L Y Cao and D J Wu Phys Rev E. 59 3880 (1999)ADSCrossRefGoogle Scholar
  20. [20]
    I G Silva, O A Rosso, M V D Vermelho and M L Lyra Commun Nonlinear Sci. 22 641(2015)CrossRefGoogle Scholar
  21. [21]
    W L Reenbohn, S S Pohlong and M C Mahato Phys Rev E. 85 031144 (2012)ADSCrossRefGoogle Scholar
  22. [22]
    X M Lv Indian J. Phys.87 903 (2013)ADSCrossRefGoogle Scholar
  23. [23]
    I Bacic, V Klinshov, V Nekorkin and M Perc EPL-Europhys Let. 124 40004(2018)ADSCrossRefGoogle Scholar
  24. [24]
    G Hu, C Min and Y Tian Acta Phys Pol A. 45 29 (2014)ADSCrossRefGoogle Scholar
  25. [25]
    B Aragie Int G Mod Phys B. 28 1550011 (2014)ADSMathSciNetCrossRefGoogle Scholar
  26. [26]
    B Zhou and D Lin Indian J. Phys.91 299 (2017)ADSCrossRefGoogle Scholar
  27. [27]
    J Liu and Y G Wang Physica A. 493 359(2018)ADSMathSciNetCrossRefGoogle Scholar
  28. [28]
    P M Shi, W Y Zhang, D Z Yuan and H F Xia Chaos Soliton Fract. 113 365(2018)ADSCrossRefGoogle Scholar
  29. [29]
    P M Shi, Y F Jin and S M Xiao Chaos. 27 113109(2017)ADSMathSciNetCrossRefGoogle Scholar
  30. [30]
    P M Shi, D Z Yuan and D Y Han G Sound Vib. 424 1(2018)ADSCrossRefGoogle Scholar
  31. [31]
    W Guo and C Dong Physica A. 416 90(2014)ADSMathSciNetCrossRefGoogle Scholar
  32. [32]
    O L Han, T Yang and C H Zeng Physica A. 408 96(2014)ADSMathSciNetCrossRefGoogle Scholar
  33. [33]
    K K Wang, L Ju and Y J Wang Chaos Soliton Fract. 108 166(2018)ADSCrossRefGoogle Scholar
  34. [34]
    K K Wang, Y J Wang, H Ye and S H Li Int J Biomath. 12 1950048(2019)MathSciNetCrossRefGoogle Scholar
  35. [35]
    R F Liu, W J Ma and J K Zeng Physica A. 517 562(2019)ADSGoogle Scholar
  36. [36]
    G Hu, G Nicolis and C Nicolis Phys Rev A. 42 2030 (1990)ADSCrossRefGoogle Scholar
  37. [37]
    J Li and J Zhang G Sound Vib. 401 139 (2017)ADSCrossRefGoogle Scholar
  38. [38]
    G Steve, L H Ivan and L André Phys Rev E. 59 3970 (1999)CrossRefGoogle Scholar
  39. [39]
    C P Jesús, G O Jose and M Manuel Phys Rev Let. 91 210601 (2003)CrossRefGoogle Scholar

Copyright information

© Indian Association for the Cultivation of Science 2020

Authors and Affiliations

  1. 1.School of Communication and Information EngineeringChongqing University of Posts and TelecommunicationsChongqingChina

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