Skip to main content
SpringerLink
Log in

Synchronization of the stochastic Fitzhugh-Nagumo equations to periodic forcing

  • Published:
Il Nuovo Cimento D

Summary

The Fitzhugh-Nagumo equations (FHN) provide a simple description of the dynamics of a large class of neurons. We characterize synchronization and stochastic resonance in this model using two complementary points of view: the signal-to-noise ratio (SNR), and the absolute as well as normalized peak heights of the interspike interval histograms (ISIHs). At low stimulus frequencies, multiple firings can occur during one period, while at high frequencies, the refractoriness precludes firing at every cycle. The behaviors of the SNR and ISIHs are thus investigated at low, medium and high frequencies to illustrate special synchronization properties of the FHN system. In particular, the behavior of the SNRvs. noise is found to be similar for forcing amplitudes just below and above that at which a 2:1 deterministic phase-locked firing solution becomes stable. Our results rely on an accurate method of estimation of the power spectrum of the point process formed by the firing times. A theoretical analysis for the shape of the simulated power spectra is also presented.

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

Similar content being viewed by others

References

  1. Alexander J. C., Doedel E. J. andOthmer H. G.,SIAM (Soc. Industr. Appl. Math.) J. Appl. Math.,50 (1990) 1373.

    Article  MATH  MathSciNet  Google Scholar 

  2. French A. S. andHolden A. V.,Kybernetik,8 (1971) 165.

    Article  Google Scholar 

  3. Moore G. P., Perkel D. H. andSegundo J. P.,Ann. Rev. Physiol.,28 (1966) 493.

    Article  Google Scholar 

  4. Longtin A., Bulsara A., Pierson D. andMoss F.,Biol. Cybern.,70 (1994) 569.

    MATH  Google Scholar 

  5. Longtin A.,J. Stat. Phys.,70 (1993) 309.

    Article  MATH  Google Scholar 

  6. Chialvo D. R. andApkarian V.,J. Stat. Phys.,70 (1993) 375.

    Article  MATH  Google Scholar 

  7. Douglass J. K., Wilkens L., Pantazelou E. andMoss F.,Nature,365 (1993) 337.

    Article  ADS  Google Scholar 

  8. McA. Sayers B.,Infering significance from biological signals, inBiomedical Engineering Systems, edited byM. Clyness andJ. Milsum (McGraw-Hill, New-York) 1970, p. 84.

    Google Scholar 

  9. Zhou T., Moss F. andJung P.,Phys. Rev. A,42 (1990) 3161.

    Article  ADS  Google Scholar 

  10. Gummer A. W.,Hearing Res.,55 (1991) 143.

    Article  Google Scholar 

  11. French A. S., Holden A. V. andStein R. B.,Kybernetik,11 (1972) 15.

    Article  Google Scholar 

  12. Wiesenfeld K., Pierson D., Pantazelou E. andMoss F.,Phys. Rev. Lett.,72 (1994) 2125.

    Article  ADS  Google Scholar 

  13. Coggshall J. C.,Kybernetik,13 (1973) 30.

    Article  Google Scholar 

  14. Hochmair-Desoyer I. J., Hochmair E. S., Motz H. andRattay F.,Neuroscience,13 (1984) 553.

    Article  Google Scholar 

  15. Motz H. andRattay F.,Neuroscience,18 (1986) 699.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Département de Physique, Université d'Ottawa, 150 Louis Pasteur, K1N 6N5, Ottawa, Ontario, Canada

    A. Longtin

Authors
  1. A. Longtin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Longtin, A. Synchronization of the stochastic Fitzhugh-Nagumo equations to periodic forcing. Il Nuovo Cimento D 17, 835–846 (1995). https://doi.org/10.1007/BF02451841

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02451841

PACS 87.10

PACS 05.40

PACS 02.50

PACS 01.30.Cc

Search

Navigation