Skip to main content
SpringerLink
Log in

Weak periodic signal detection by sine-Wiener-noise-induced resonance in the FitzHugh–Nagumo neuron

  • Research Article
  • Published:
Cognitive Neurodynamics Aims and scope Submit manuscript

Abstract

Based on the FitzHugh–Nagumo (FHN) neuron model subjected to sine-Wiener (SW) noise, impacts of SW noise on weak periodic signal detection are investigated by calculating response measure Q for characterizing synchronization between the input signal and the output temporal activities of the neuron. It is numerically demonstrated that the response measure Q can achieve the optimal value under appropriate and moderate intensity or correlation time of SW noise, suggesting the occurrence of SW-noise-induced stochastic resonance. Furthermore, the optimal value of Q is sensitive to correlation time. Consequently, the correlation time of SW noise has a great influence on the performance of signal detection in the FHN neuron.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6

Similar content being viewed by others

References

  • Benzi R, Sutera A, Vulpiani A (2004) The mechanism of stochastic resonance. J Phys A: Gen Phys 14:L453–L457

    Article  Google Scholar 

  • Bezrukov SM, Vodyanoy I (1995) Noise-induced enhancement of signal transduction across voltage-dependent ion channels. Nature 378:362–364

    Article  CAS  PubMed  Google Scholar 

  • Cai GQ, Wu C (2004) Modeling of bounded stochastic processes. Probab Eng Mech 19:197–203

    Article  Google Scholar 

  • Ermentrout GB, Galán RF, Urban NN (2008) Reliability, synchrony and noise. Trends Neurosci 31:428–434

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Faisal AA, Selen LPJ, Wolpert DM (2008) Noise in the nervous system. Nat Rev Neurosci 9:292–303

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Fox RF, Gatland IR, Roy R, Vemuri G (1988) Fast, accurate algorithm for numerical simulation of exponentially correlated colored noise. Phys Rev A 38:5938–5940

    Article  CAS  Google Scholar 

  • Gammaitoni L, Hänggi P, Jung P, Marchesoni F (1998) Stochastic resonance. Rev Mod Phys 70:45–105

    Article  Google Scholar 

  • Gang H, Ditzinger T, Ning CZ, Haken H (1993) Stochastic resonance without external periodic force. Phys Rev Lett 71:807–810

    Article  CAS  PubMed  Google Scholar 

  • Ge M, Jia Y, Xu Y, Yang L (2017) Mode transition in electrical activities of neuron driven by high and low frequency stimulus in the presence of electromagnetic induction and radiation. Nonlinear Dyn 91:515–523

    Article  Google Scholar 

  • Guo W, Mei DC (2014) Stochastic resonance in a tumor–immune system subject to bounded noises and time delay. Phys A 416:90–98

    Article  Google Scholar 

  • Guo W, Du LC, Mei DC (2012a) Coherence and spike death induced by bounded noise and delayed feedback in an excitable system. Eur Phys J B 85:1–7

    Article  Google Scholar 

  • Guo W, Du LC, Mei DC (2012b) Transitions induced by time delays and cross-correlated sine-Wiener noises in a tumor–immune system interplay. Phys A 391:1270–1280

    Article  Google Scholar 

  • Hänggi P (2002) Stochastic resonance in biology. How noise can enhance detection of weak signals and help improve biological information processing. Chemphyschem A Eur J Chem Phys Phys Chem 3:285–290

    Article  Google Scholar 

  • Kang XS, Liang XM, Lü HP (2013) Enhanced response to subthreshold signals by phase noise in a Hodgkin–Huxley Neuron. Chinphyslett 30:018701–018704

    Google Scholar 

  • Kish EA, Granqvist CG, Der A, Kish LB (2015) Lognormal distribution of firing time and rate from a single neuron? Cogn Neurodyn 9:459–462

    Article  PubMed  PubMed Central  Google Scholar 

  • Liang XM, Liu ZH (2016) Effect of initial phase diversity on signal detection in excitable systems. Sci China Technol Sci 59:376–386

    Article  Google Scholar 

  • Liang X, Dhamala M, Zhao L, Liu Z (2010) Phase-disorder-induced double resonance of neuronal activity. Phys Rev E 82:010902–010905

    Article  Google Scholar 

  • Liang X, Zhao L, Liu Z (2011) Phase-noise-induced resonance in a single neuronal system. Phys Rev E 84:031916–031920

    Article  Google Scholar 

  • Lu L, Jia Y, Liu W, Yang LJ (2017) Mixed stimulus-induced mode selection in neural activity driven by high and low frequency current under electromagnetic radiation. Complexity 2017:7628537

    Google Scholar 

  • Ma J, Tang J (2017) A review for dynamics in neuron and neuronal network. Nonlinear Dyn 89:1569–1578

    Article  Google Scholar 

  • Ning LJ, Liu P (2016) The effect of sine-Wiener noises on transition in a genotype selection model with time delays. Eur Phys J B 89:201

    Article  Google Scholar 

  • Pikovsky AS, Kurths J (1997) Coherence resonance in a noise-driven excitable system. Phys Rev Lett 78:775–778

    Article  CAS  Google Scholar 

  • Qu J, Wang R, Du Y, Cao J (2012) Synchronization study in ring-like and grid-like neuronal networks. Cogn Neurodyn 6:21–31

    Article  PubMed  Google Scholar 

  • Shi JC, Luo M, Huang CS (2017) Cooperative effect of random and time-periodic coupling strength on synchronization transitions in one-way coupled neural system: mean field approach. Cogn Neurodyn 11:383–390

    Article  Google Scholar 

  • Stacey WC, Durand DM (2000) Stochastic resonance improves signal detection in hippocampal CA1 neurons. J Neurophysiol 83:1394–1402

    Article  CAS  PubMed  Google Scholar 

  • Volkov EI, Ullner E, Zaikin AA, Kurths J (2003) Oscillatory amplification of stochastic resonance in excitable systems. Phys Rev E 68:026214–026220

    Article  CAS  Google Scholar 

  • Wang RB, Wang GZ, Zheng JC (2014) An exploration of the range of noise intensity that affects the membrane potential of neurons. Abstr Appl Anal 2014:801642–801652

    Google Scholar 

  • Wang C, Guo S, Xu Y, Tang J, Alzahrani F, Hobiny A (2017a) Formation of autapse connected to neuron and its biological function. Complexity 2017:5436737

    Google Scholar 

  • Wang LF, Qiu K, Jia Y (2017b) Effects of time delays in a mathematical bone model. Chin Phys B 26:030503–030509

    Article  Google Scholar 

  • Wang Y, Ma J, Xu Y, Wu F, Zhou P (2017c) The electrical activity of neurons subject to electromagnetic induction and gaussian white noise. Int J Bifurc Chaos 27:1750030–1750041

    Article  Google Scholar 

  • Wiesenfeld K, Moss F (1995) Stochastic resonance and the benefits of noise: from ice ages to crayfish and SQUIDs. Nature 373:33–36

    Article  CAS  PubMed  Google Scholar 

  • Wu F, Wang C, Jin W, Ma J (2017) Dynamical responses in a new neuron model subjected to electromagnetic induction and phase noise. Phys A 469:81–88

    Article  Google Scholar 

  • Xu Y, Jia Y, Ge M, Lu L, Yang LJ, Zhan X (2017) Effects of ion channel blocks on electrical activity of stochastic Hodgkin-Huxley neural network under electromagnetic induction. Neurocomputing. https://doi.org/10.1016/j.neucom.2017.12.036

    Google Scholar 

  • Yang H, Ning LJ (2017) Phase transitions induced by time-delay and different noises. Nonlinear Dyn 88:2427–2433

    Article  Google Scholar 

  • Yang LJ, Liu WH, Yi M, Wang CJ, Zhu QM, Zhan X, Jia Y (2012) Vibrational resonance induced by transition of phase-locking modes in excitable systems. Phys Rev E 86:016209–016215

    Article  Google Scholar 

  • Yao C, Zhan M (2010) Signal transmission by vibrational resonance in one-way coupled bistable systems. Phys Rev E 81:061129–061136

    Article  Google Scholar 

  • Yao C, He Z, Luo J, Shuai J (2015) Resonance induced by a spatially periodic force in the reaction-diffusion system. Phys Rev E 91:052901–052906

    Article  Google Scholar 

  • Yao C, Ma J, Li C, He Z (2016) The effect of process delay on dynamical behaviors in a self-feedback nonlinear oscillator. Commun Nonlinear Sci Numer Simul 39:99–107

    Article  Google Scholar 

  • Yao Y, Deng H, Ma C, Yi M, Ma J (2017a) Impact of bounded noise and rewiring on the formation and instability of spiral waves in a small-world network of Hodgkin–Huxley neurons. PLoS ONE 12:e0171273

    Article  PubMed  PubMed Central  Google Scholar 

  • Yao Y, Deng H, Yi M, Ma J (2017b) Impact of bounded noise on the formation and instability of spiral wave in a 2D Lattice of neurons. Sci Rep 7:43151

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  • Yao Y, Yi M, Hou D (2017c) Coherence resonance induced by cross-correlated sine-Wiener noises in the FitzHugh–Nagumo neurons. Int J Mod Phys 31:1750204

    Article  Google Scholar 

  • Yilmaz E, Ozer M (2015) Delayed feedback and detection of weak periodic signals in a stochastic Hodgkin–Huxley neuron. Phys A 421:455–462

    Article  Google Scholar 

  • Zhao J, Deng B, Qin Y, Men C, Wang J, Wei X, Sun J (2017) Weak electric fields detectability in a noisy neural network. Cogn Neurodyn 11:81–90

    Article  PubMed  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 31601071).

Author information

Authors and Affiliations

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

    Yuangen Yao

  2. Department of Physics, Lanzhou University of Technology, Lanzhou, China

    Jun Ma

Authors
  1. Yuangen Yao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jun Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yuangen Yao.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yao, Y., Ma, J. Weak periodic signal detection by sine-Wiener-noise-induced resonance in the FitzHugh–Nagumo neuron. Cogn Neurodyn 12, 343–349 (2018). https://doi.org/10.1007/s11571-018-9475-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11571-018-9475-3

Keywords

Search

Navigation