Journal of Mathematical Biology

, Volume 67, Issue 2, pp 239–259 | Cite as

The Morris–Lecar neuron model embeds a leaky integrate-and-fire model

  • Susanne Ditlevsen
  • Priscilla Greenwood
Open Access


We show that the stochastic Morris–Lecar neuron, in a neighborhood of its stable point, can be approximated by a two-dimensional Ornstein–Uhlenbeck (OU) modulation of a constant circular motion. The associated radial OU process is an example of a leaky integrate-and-fire (LIF) model prior to firing. A new model constructed from a radial OU process together with a simple firing mechanism based on detailed Morris–Lecar firing statistics reproduces the Morris–Lecar Interspike Interval (ISI) distribution, and has the computational advantages of a LIF. The result justifies the large amount of attention paid to the LIF models.


Stochastic dynamics Diffusions Interspike intervals Conditional firing probability 

Mathematics Subject Classification

60G17 92Bxx 37N25 92C20 



S. Ditlevsen was supported by the Danish Council for Independent Research|Natural Sciences. P. Greenwood was supported by the Statistical and Applied Mathematical Sciences Institute, Research Triangle Park, N.C., and the Mathematical, Computational and Modeling Sciences Center at Arizona State University. The Villum Kann Rasmussen foundation supported a 4 months visiting professorship for P. Greenwood at University of Copenhagen.

Open Access

This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.


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Copyright information

© The Author(s) 2012

Authors and Affiliations

  1. 1.Department of Mathematical SciencesUniversity of CopenhagenCopenhagenDenmark
  2. 2.Mathematics Annex 1208VancouverCanada

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