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

Jack Cowan
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Jack Cowan: University of Chicago, Department of Mathematics

Chapter Chapter 2 in Neural Fields, 2014, pp 47-96 from Springer

Abstract: 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

Keywords: Large-scale Brain Activity; Wilson-Cowan Equations; System Size Expansion; Master Equation; Moment Generating Functions (MGF) (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-54593-1_2

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DOI: 10.1007/978-3-642-54593-1_2

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