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Preprints, Working Papers, ... Year : 2010

Stochastic firing rate models

Abstract

We review a recent approach to the mean-field limits in neural networks that takes into account the stochastic nature of input current and the uncertainty in synaptic coupling. This approach was proved to be a rigorous limit of the network equations in a general setting, and we express here the results in a more customary and simpler framework. We propose a heuristic argument to derive these equations providing a more intuitive understanding of their origin. These equations are characterized by a strong coupling between the different moments of the solutions. We analyse the equations, present an algorithm to simulate the solutions of these mean-field equations, and investigate numerically the equations. In particular, we build a bridge between these equations and Sompolinsky and collaborators approach (1988, 1990), and show how the coupling between the mean and the covariance function deviates from customary approaches.

Dates and versions

inria-00534332 , version 1 (09-11-2010)

Identifiers

  • HAL Id : inria-00534332 , version 1
  • ARXIV : 1001.3872

Cite

Jonathan Touboul, Bard Ermentrout, Olivier Faugeras, Bruno Cessac. Stochastic firing rate models. 2010. ⟨inria-00534332⟩
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