Skip to main content
SpringerLink
Log in

A Wiener Neuronal Model with Refractoriness

  • Conference paper
Computer Aided Systems Theory – EUROCAST 2005 (EUROCAST 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3643))

Included in the following conference series:

Abstract

A mathematical characterization of the membrane potential as an instantaneous return process in the presence of random refractoriness is investigated for the Wiener neuronal model. In the case of constant refractoriness, simple closed form expressions are obtained.

This work has been performed under partial support by MIUR (PRIN 2003) and by GNCS-INdAM.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Cox, D.R., Miller, H.D.: The Theory of Stochastic Processes, Methuen, London (1970)

    Google Scholar 

  2. Esposito, G., Giorno, V., Nobile, A.G., Ricciardi, L.M., Valerio, C.: Interspike analysis for a single neuron’s activity in presence of refractoriness. In: Trappl, R. (ed.) Cybernetics and Systems, vol. 1, pp. 199–204. Austrian Society for Cybernetics Studies, Vienna (2004)

    Google Scholar 

  3. Gerstein, G.L., Mandelbrot, B.: Random walk models for the spike activity of a single neuron. Biophys. J. 4, 41–68 (1964)

    Article  Google Scholar 

  4. Giorno, V., Nobile, A.G., Ricciardi, L.M.: On the moments of firing numbers in diffusion neuronal models with refractoriness. In: Mira, J., Álvarez, J.R. (eds.) IWINAC 2005. LNCS, vol. 3561, pp. 186–194. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Ricciardi, L.M., Di Crescenzo, A., Giorno, V., Nobile, A.G.: An outline of theoretical and algorithmic approaches to first passage time problems with applications to biological modeling. Math. Japonica 50(2), 247–322 (1999)

    MATH  Google Scholar 

  6. Ricciardi, L.M., Esposito, G., Giorno, V., Valerio, C.: Modeling Neuronal Firing in the Presence of Refractoriness. In: Mira, J., Álvarez, J.R. (eds.) IWANN 2003. LNCS, vol. 2686, pp. 1–8. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, Università di Salerno, Via Ponte don Melillo, 84084, Fisciano (SA), Italy

    Virginia Giorno & Amelia G. Nobile

  2. Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Via Cintia, 80126, Napoli, Italy

    Luigi M. Ricciardi

Authors
  1. Virginia Giorno
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Amelia G. Nobile
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Luigi M. Ricciardi
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Instituto Universitario de Ciencias y Tecnologícas Cibernéticas, Universidad de Las Palmas de Gran Canaria, Campus de Tafira, 35017, Las Palmas de Gran Canaria,, Las Palmas, Spain

    Roberto Moreno Díaz

  2. Systems Theory, Johannes Kepler University Linz, Altenbergerstrasse 69, A-4040, Linz, Austria

    Franz Pichler

  3. Universidad de Las Palmas de Gran Canaria, Instituto Universitario de Ciencias y Tecnologícas Cibernéticas, Campus de Tafira, 35017, Las Palmas de Gran Canaria, Las Palmas, Spain

    Alexis Quesada Arencibia

Rights and permissions

Reprints and permissions

Copyright information

© 2005 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Giorno, V., Nobile, A.G., Ricciardi, L.M. (2005). A Wiener Neuronal Model with Refractoriness. In: Moreno Díaz, R., Pichler, F., Quesada Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2005. EUROCAST 2005. Lecture Notes in Computer Science, vol 3643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11556985_55

Download citation

  • DOI: https://doi.org/10.1007/11556985_55

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29002-5

  • Online ISBN: 978-3-540-31829-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation