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Modeling cortical dynamics with Wilson-Cowan equations

Experimental data collected over the last decade indicates that there exist at least two distinct modes of cortical response to stimuli. In mode 1 a low intensity stimulus triggers a wave that propagates at a velocity of about 0.3 m/sec, with an amplitude that decays exponentially. In mode 2 a high intensity stimulus triggers a larger response that remains local, and does not propagate to neighboring regions. Other data indicate that unstimulated or resting cortex exhibits pair correlations between neighboring cells, the amplitudes of which decay slowly with distance, whereas stimulated cortex exhibits pair correlations whose amplitude falls of rapidly with distance. Here we show how the mean-field Wilson-Cowan equations can account precisely for the two modes of cortical response, and how stochastic Wilson-Cowan equations can account for the behavior of the pair correlations. We will present these results after outlining the basic properties of both the mean-field and stochastic equations.

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Correspondence to Jack Cowan.

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This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Creative Commons Public Domain Dedication waiver ( applies to the data made available in this article, unless otherwise stated.

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Cowan, J. Modeling cortical dynamics with Wilson-Cowan equations. BMC Neurosci 16, A1 (2015).

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  • Experimental Data
  • Animal Model
  • High Intensity
  • Basic Property
  • Neighboring Cell