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.
This work has been performed under partial support by F.A.R.O Project (Finanziamenti per l’Avvio di Ricerche Originali, III tornata) “Controllo e stabilità di processi diffusivi nell’ambiente”, Polo delle Scienze e Tecnologie, Università degli Studi di Napoli Federico II.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arnold, L.: Stochastic Differential Equations: Theory and Applications. Wiley and Sons, New York (1974)
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)
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)
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)
Burkitt, A.N.: A review of the integrate-and-fire neuron model: I. Homogeneous synaptic input. Biol. Cybern. 95, 1–19 (2006)
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)
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)
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)
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)
Golomb, D., Ermentrout, G.B.: Bistability in pulse propagation in networks of excitatory and inhibitory populations. Phys. Rev. Lett. 86(18), 4179–4182 (2001)
Sakaguchi, H.: Oscillatory phase transition and pulse propagation in noisy integrate-and-fire neurons. Phys. Rev. E. Stat. Nonlin. Soft. Matter Phys. (2004)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Buonocore, A., Caputo, L., Carfora, M.F., Pirozzi, E. (2013). On the Dynamics of a Couple of Mutually Interacting Neurons. In: Moreno-Díaz, R., Pichler, F., Quesada-Arencibia, A. (eds) Computer Aided Systems Theory - EUROCAST 2013. EUROCAST 2013. Lecture Notes in Computer Science, vol 8111. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53856-8_5
Download citation
DOI: https://doi.org/10.1007/978-3-642-53856-8_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-53855-1
Online ISBN: 978-3-642-53856-8
eBook Packages: Computer ScienceComputer Science (R0)