Tutorial on Neural Field Theory

Stephen Coombes (), Peter beim Graben and Roland Potthast
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Stephen Coombes: University of Nottingham, School of Mathematical Sciences
Peter beim Graben: Bernstein Center for Computational Neuroscience
Roland Potthast: University of Reading, Department of Mathematics

Chapter Chapter 1 in Neural Fields, 2014, pp 1-43 from Springer

Abstract: Abstract The tools of dynamical systems theory are having an increasing impact on our understanding of patterns of neural activity. In this tutorial chapter we describe how to build tractable tissue level models that maintain a strong link with biophysical reality. These models typically take the form of nonlinear integro-differential equations. Their non-local nature has led to the development of a set of analytical and numerical tools for the study of spatiotemporal patterns, based around natural extensions of those used for local differential equation models. We present an overview of these techniques, covering Turing instability analysis, amplitude equations Amplitude equations , and travelling waves. Finally we address inverse problems Inverse problems for neural fields to train synaptic weight kernels from prescribed field dynamics.

Keywords: Neural Field Model; Turing Instability; Amplitude Equations; Firing Rate Function; Axonal Delay (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_1

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DOI: 10.1007/978-3-642-54593-1_1

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