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

In: Neural Fields

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  • Jack Cowan

    (University of Chicago, Department of Mathematics)

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. Oscillations

Suggested Citation

  • Jack Cowan, 2014. "A Personal Account of the Development of the Field Theory of Large-Scale Brain Activity from 1945 Onward," Springer Books, in: Stephen Coombes & Peter beim Graben & Roland Potthast & James Wright (ed.), Neural Fields, edition 127, chapter 0, pages 47-96, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-54593-1_2
    DOI: 10.1007/978-3-642-54593-1_2
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