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. 2020 May 1;123(5):1645-1656.
doi: 10.1152/jn.00404.2019. Epub 2020 Mar 18.

Before and beyond the Wilson-Cowan equations

Carson C Chow  1 , Yahya Karimipanah  1
Affiliations

Before and beyond the Wilson-Cowan equations

Carson C Chow et al. J Neurophysiol. .

Abstract

The Wilson-Cowan equations represent a landmark in the history of computational neuroscience. Along with the insights Wilson and Cowan offered for neuroscience, they crystallized an approach to modeling neural dynamics and brain function. Although their iconic equations are used in various guises today, the ideas that led to their formulation and the relationship to other approaches are not well known. Here, we give a little context to some of the biological and theoretical concepts that lead to the Wilson-Cowan equations and discuss how to extend beyond them.

Keywords: computational neuroscience; mean field theory; neural field theory; population activity; rate models.

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Conflict of interest statement

No conflicts of interest, financial or otherwise, are declared by the authors.

References

    1. Amari S. Dynamics of pattern formation in lateral-inhibition type neural fields. Biol Cybern 27: 77–87, 1977. doi:10.1007/BF00337259. - DOI - PubMed
    1. Amari S. Field theory of self-organizing neural nets. IEEE Trans Syst Man Cybern SMC-13: 741–748, 1983. doi:10.1109/TSMC.1983.6313068. - DOI
    1. Amit DJ, Gutfreund H, Sompolinsky H. Spin-glass models of neural networks. Phys Rev A Gen Phys 32: 1007–1018, 1985. doi:10.1103/PhysRevA.32.1007. - DOI - PubMed
    1. Averbeck BB, Latham PE, Pouget A. Neural correlations, population coding and computation. Nat Rev Neurosci 7: 358–366, 2006. doi:10.1038/nrn1888. - DOI - PubMed
    1. Ben-Yishai R, Bar-Or RL, Sompolinsky H. Theory of orientation tuning in visual cortex. Proc Natl Acad Sci USA 92: 3844–3848, 1995. doi:10.1073/pnas.92.9.3844. - DOI - PMC - PubMed

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