Advertisement

On the Dynamics of a Couple of Mutually Interacting Neurons

  • A. Buonocore
  • L. Caputo
  • M. F. Carfora
  • E. Pirozzi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8111)

Abstract

A model for describing the dynamics of two mutually interacting neurons is considered. In such a context, maintaining statements of the Leaky Integrate-and-Fire framework, we include a random component in the synaptic current, whose role is to modify the equilibrium point of the membrane potential of one of the two neurons when a spike of the other one occurs. We give an approximation for the interspike time interval probability density function of both neurons within any parametric configurations driving the evolution of the membrane potentials in the so-called subthreshold regimen.

Keywords

Membrane Potential Synaptic Current Asymptotic Regimen Decay Time Constant Autocovariance Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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 and Sons, New York (1974)zbMATHGoogle Scholar
  2. 2.
    Buonocore, A., Nobile, A.G., Ricciardi, L.M.: A new integral equation for the evaluation of first-passage-time probability densities. Advances in Applied Probability 19, 784–800 (1987)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Buonocore, A., Caputo, L., Pirozzi, E., Ricciardi, L.M.: The first passage time problem for Gauss-diffusion processes: algorithmic approaches and applications to LIF neuronal model. Methodol. Comput. Appl. Probab. 13(1), 29–57 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Buonocore, A., Caputo, L., Pirozzi, E.: Gauss-Diffusion Processes for Modeling the Dynamics of a Couple of Interacting Neurons. Mathematical Biosciences and Engineering (in press)Google Scholar
  5. 5.
    Burkitt, A.N.: A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input. Biol. Cybern. 95, 1–19 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Burkitt, A.N.: A review of the integrate-and-fire neuron model: II. Inhomogeneous synaptic input and network properties. Biol. Cybern. 95, 97–112 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Di Nardo, E., Nobile, A.G., Pirozzi, E., Ricciardi, L.M.: A computational approach to first-passage-time problems for Gauss-Markov processes. Adv. Appl. Prob. 33, 453–482 (2001)CrossRefzbMATHGoogle Scholar
  8. 8.
    Giorno, V., Nobile, A.G., Ricciardi, L.M.: On the asymptotic behaviour of first-passage-time densities for one-dimensional diffusion processes and varying boundaries. Adv. Appl. Prob. 22, 883–914 (1990)MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Lansky, P., Sanda, P., He, J.: The parameters of the stochastic leaky integrate-and-fire neuronal model. J. Comp. NeuroSciences 21(2), 211–223 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Golomb, D., Ermentrout, G.B.: Bistability in pulse propagation in networks of excitatory and inhibitory populations. Phys. Rev. Lett. 86(18), 4179–4182 (2001)CrossRefGoogle Scholar
  11. 11.
    Sakaguchi, H.: Oscillatory phase transition and pulse propagation in noisy integrate-and-fire neurons. Phys. Rev. E. Stat. Nonlin. Soft. Matter Phys. (2004)Google Scholar
  12. 12.
    Sakaguchi, H., Tobiishi, S.: Synchronization and spindle oscillation in noisy integrate-and-fire-or-burst neurons with inhibitory coupling. Progress of Theoretical Physics 114(3), 1–18 (2005)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • A. Buonocore
    • 1
  • L. Caputo
    • 1
  • M. F. Carfora
    • 2
  • E. Pirozzi
    • 1
  1. 1.Dipartimento di Matematica e ApplicazioniUniversità di Napoli Federico IINapoliItaly
  2. 2.Istituto per le Applicazioni del Calcolo “Mauro Picone”Consiglio Nazionale delle RicercheNapoliItaly

Personalised recommendations