Abstract
We derive a dynamical equation for the spike emission rate ν(t) of a homogeneous population of Integrate-and-Fire (IF) neurons, in an “extended” mean-field approximation (i.e., taking into account both the mean and the variance of the afferent current). Conditions for stability and characteristic times of the population transient response are investigated, and both are shown to be naturally expressed in terms of single neuron current-to-rate transfer function. Finite-size effects are incorporated by a stochastic extension of the mean-field equations and the associated Fokker-Planck formalism, and their implications for the frequency response of the population activity is illustrated through the power spectral density of ν(t). The role of synaptic delays in spike transmission is studied for an arbitrary distribution of delays.
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.
Similar content being viewed by others
References
L. F. Abbot and Carl van Vreeswijk. Asynchronous states in networks of pulse-coupled oscillators. Phys. Rev. E, 48(2):1483–1490, 1993.
Daniel J. Amit and Nicolas Brunel. Model of global spontaneous activity and local structured (learned) delay activity during delay periods in cerebral cortex. Cerebral Cortex, 7:237–252, 1997a.
Daniel J. Amit and Misha Tsodyks. Quantitative study of attractor neural network retrieving at low spike rates: I. substrate-spikes, and neuronal gain. Network, 2:259, 1991.
Nicolas Brunel and Vincent Hakim. Fast Global Oscillations in Netwoks of Integrate-and-Fire Neurons with Low Firing Rates. Neural Comput., 11:1621–1671, 1999.
Stefano Fusi and Maurizio Mattia. Collective Behavior of Networks with Linear (VLSI) Integrate-and-Fire Neurons. Neural Comput, 11(3):633–653, apr 1999.
Bruce W. Knight, Dimitri Manin, and Lawrence Sirovich. Dynamical models of interacting neuron propulations in visual cortex. In E. C. Gerf, editor, Proceedings of Symposium on Robotics and Cybernetics, Lille-France, July 9-12, 1996.
Maurizio Mattia and Paolo Del Giudice. On the population dynamics of interacting spiking neurons. submitted (draft available in http://neural.iss.infn.it), 2001.
Duane Q. Nykamp and Daniel Tranchina. A population density approach that facilitates large-scale modeling of neural networks: analysis and an application to orientation tuning. J. Comput. Neurosci., 8:19–50, 2000.
Hannes Risken. The Fokker-Planck Equation: Methods of Solution and Applications. Springer-Verlag, Berlin, 1984.
Alessandro Treves. Mean-field analysis of neuronal spike dynamics. Network, 4:259–284, 1993.
Henry C. Tuckwell. Introduction to Theoretical Neurobiology, volume 2. Cambridge University Press, 1988.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Mattia, M., Del Giudice, P. (2002). Mean-Field Population Dynamics of Spiking Neurons with Random Synaptic Delays. In: Dorronsoro, J.R. (eds) Artificial Neural Networks — ICANN 2002. ICANN 2002. Lecture Notes in Computer Science, vol 2415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46084-5_19
Download citation
DOI: https://doi.org/10.1007/3-540-46084-5_19
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44074-1
Online ISBN: 978-3-540-46084-8
eBook Packages: Springer Book Archive