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A Personal Account of the Development of the Field Theory of Large-Scale Brain Activity from 1945 Onward

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Neural Fields

Abstract

In this paper I give my personal perspective on the development of a field theory of large-scale brain activity. I review early work by Pitts, Wiener, Beurle and others, and give an account of the development of the mean-field Wilson-Cowan equations. I then outline my reasons for trying to develop a stochastic version of these equations, and recall the steps leading to the discovery that one can use field theory and the van Kampen system-size expansion of a neural master equation to obtain stochastic Wilson-Cowan equations. I then describe how stochastic neural field theory led to the discovery that there is a directed percolation phase transition in large-scale brain activity, and how the stochastic Wilson-Cowan equations can provide insight into many aspects of large-scale brain activity, such as the generation of fluctuation-driven avalanches and oscillations.

Ah, but a man’s reach should exceed his grasp, Or what’s a heaven for?

Robert Browning (1855)

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Acknowledgements

I would like to acknowledge with thanks the financial support from ONR on two separate contracts, and that from the Grant Foundation and the James S. McDonnell Foundation, which greatly facilitated the development of this work. I will always appreciate the many contributions to this work made by my Postdoctoral Fellow and later colleague Hugh Wilson in the early days of this work, and the more recent contributions of my graduate students Toru Ohira, Michael Buice, Edward Wallace and Marc Benayoun, and of my collaborators Paul Bressloff and Wim van Drongelen, and of Nigel Goldenfeld and his graduate student Tom Butler at the University of Illinois, Urbana-Champaign, not to speak of the many other colleagues at the University of Chicago who, over the years since 1967, have provided much stimulation and constructive criticism.

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  1. Department of Mathematics, University of Chicago, 5734 S. University Ave., Chicago, IL, 60637, USA

    Jack Cowan

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  1. Jack Cowan
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  1. School of Mathematical Sciences, University of Nottingham, Nottingham, United Kingdom

    Stephen Coombes

  2. Department of German Studies and Linguistics, Humboldt-Universität zu Berlin, Berlin, Germany

    Peter beim Graben

  3. Department of Mathematics, University of Reading, Reading, United Kingdom

    Roland Potthast

  4. School of Medicine, University of Auckland, Auckland, New Zealand

    James Wright

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Cowan, J. (2014). A Personal Account of the Development of the Field Theory of Large-Scale Brain Activity from 1945 Onward. In: Coombes, S., beim Graben, P., Potthast, R., Wright, J. (eds) Neural Fields. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-54593-1_2

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