Advertisement

Ghost Stochastic Resonance for a Neuron with a Pair of Periodic Inputs

  • Maria Teresa Giraudo
  • Laura Sacerdote
  • Alessandro Sicco
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4729)

Abstract

A small network like that proposed in [8] and [9] is studied when a pair of periodic signals are carried by the two different input neurons to verify the arising of ghost stochastic resonance phenomena in the third processing neuron. Suitable modifications of the stochastic leaky integrate-and-fire model are employed to describe the membrane potential of the input neurons while the processing neuron is modeled by means of a jump-diffusion process. A stochastic resonance behavior is detected for the processing neuron in correspondence with the ”ghost” frequencies both in the harmonic and in the anharmonic case. The range of parameter values under which this behavior occurs is specified and an interpretation of the coincidence detection mechanism involved is provided.

Keywords

Leaky integrate-and-fire model fundamental frequency jump-diffusion process coincidence detection 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Arnold, L.: Stochastic Differential Equations: Theory and Applications. Wiley, New York (1974)zbMATHGoogle Scholar
  2. 2.
    Balenzuela, P., Garcia-Ojalvo, J.: Neural mechanism for binaural pitch perception via ghost stochastic resonance. Chaos 15(023903), 1–8 (2005)Google Scholar
  3. 3.
    Chialvo, D.R., Calvo, O., Gonzales, D.L., Piro, O., Savino, G.V.: Subharmonic stochastic synchronization and resonance in neuronal systems. Phys. Rev. E 65(5) (2002), Art. No. 050902(R)Google Scholar
  4. 4.
    Chialvo, D.R.: How we hear what is not there: A neural mechanism for the missing fundamental illusion. Chaos 13(4), 1226–1230 (2003)CrossRefGoogle Scholar
  5. 5.
    Giraudo, M.T., Sacerdote, L.: Ghost stochastic resonance for a single neuron model. Sc. Math. Jap. 64(2), 299–312 (2006)zbMATHMathSciNetGoogle Scholar
  6. 6.
    Ricciardi, L.M., Di Crescenzo, A., Giorno, V., Nobile, A.G.: An outline of theoretical and algorithmic approaches to first passage time problems with application to biological modeling. Math. Japonica 50(2), 247–322 (1999)zbMATHGoogle Scholar
  7. 7.
    Ricciardi, L.M.: On the trasformation of diffusion processes into the Wiener process. J. Math. Anal. Appl. 54, 185–199 (1976)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Sirovich, R.: Mathematical models for the study of synchronization phenomena in neuronal networks. PhD Thesis, University of Torino and University of Grenoble (2006)Google Scholar
  9. 9.
    Sacerdote, L., Sirovich, R., Villa, A.E.P.: Multimodal inter-spike interval distribution in a jump diffusion neuronal model, pp. 1–22 (preprint)Google Scholar
  10. 10.
    Shimokawa, T., Pakdaman, K., Sato, S.: Time-scale matching in the response of a stochastic leaky integrate-and-fire neuron model to periodic stimulus with additive noise. Phys. Rev. E 59(3), 3427–3443 (1999)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Maria Teresa Giraudo
    • 1
  • Laura Sacerdote
    • 1
  • Alessandro Sicco
    • 1
  1. 1.Dept. of Mathematics University of Torino, Via C.Alberto 10, 10123 TorinoItaly

Personalised recommendations