Advertisement

On Time Non-homogeneous Feller-Type Diffusion Process in Neuronal Modeling

  • Amelia G. Nobile
  • Enrica Pirozzi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9520)

Abstract

Time non-homogeneous Feller-type and Ornstein-Uhlenbeck diffusion processes are considered for modeling the neuronal activity in the presence of time-varying input signals. In particular, the first passage time (FPT) problem is analyzed for both processes and the averages of FPT through a constant boundary are compared for a constant input signal and for different choices of involved parameters.

References

  1. 1.
    Buonocore, A., Caputo, L., Pirozzi, E., Ricciardi, L.M.: On a stochastic leaky integrate-and-fire neuronal model. Neural Comput. 22(10), 2558–2585 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Buonocore, A., Caputo, L., Nobile, A.G., Pirozzi, E.: Gauss-Markov processes in the presence of a reflecting boundary and applications in neuronal models. Appl. Math. Comput. 232, 799–809 (2014)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Burkitt, A.N.: A review of the integrate-and-fire neuron model. II. Inhomogeneous synaptic input and network properties. Biol. Cybern. 95(2), 97–112 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Ditlevsen, S., Lánský, P.: Estimation of the input parameters in the Feller neuronal model. Phys. Rev. E 73(061910), 1–9 (2006)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Giorno, V., Nobile, A.G., Ricciardi, L.M., Sato, S.: On the evaluation of first-passage-time probability densities via non-singular integral equation. Adv. Appl. Prob. 21, 20–36 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Giorno, V., Spina, S.: On the return process with refractoriness for a non-homogeneous Ornstein-Uhlenbeck neuronal model. Math. Biosci. Eng. 11(2), 285–302 (2014)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Giraudo, M.T., Sacerdote, L.: Effect of periodic stimulus on a neuronal diffusion model with signal-dependent noise. BioSystems 79, 73–81 (2005)CrossRefGoogle Scholar
  8. 8.
    Inoue, J., Doi, S.: Sensitive dependence of the coefficient of variation of interspike intervals on the lower boundary of membrane potential for leaky integrate-and.fire neuron model. BioSystems 87, 49–57 (2007)CrossRefGoogle Scholar
  9. 9.
    Kobayashi, R., Shinomoto, S., Lánský, P.: Estimation of time-dependent input from neuronal membrane potential. Neural Comput. 23, 3070–3093 (2011)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Lánský, P., Ditlevsen, S.: A review of the methods for signal estimation in stochastic diffusion leaky integrate-and-fire neuronal models. Biol. Cybern. 99, 253–262 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    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)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Dipartimento di Studi e Ricerche Aziendali (Management and Information Technology)Università di SalernoFiscianoItaly
  2. 2.Dipartimento di Matematica e ApplicazioniUniversità di Napoli Federico IINapoliItaly

Personalised recommendations