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Tutorial on Neural Field Theory

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Neural Fields

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 , and travelling waves. Finally we address inverse problems for neural fields to train synaptic weight kernels from prescribed field dynamics.

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Acknowledgements

SC would like to thank Ruth Smith for a careful reading of the material in this chapter. PbG gratefully acknowledges support from a DFG Heisenberg fellowship (GR 3711/1-2). The authors also thank EPSRC and the Centre for Cognitive Neuroscience and Neurodynamics (CINN) of the University of Reading, UK, for supporting the discussion on this tutorial by funding the 2nd International Conference on Neural Field Theory in April 2012 in Reading.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Nottingham, NG7 2RD, Nottingham, UK

    Stephen Coombes

  2. Bernstein Center for Computational Neuroscience, 10115, Berlin, Germany

    Peter beim Graben

  3. Department of Mathematics, University of Reading, RG6 6AX, Reading, UK

    Roland Potthast

  4. Deutscher Wetterdienst, Offenbach, Germany

    Roland Potthast

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  1. Stephen Coombes
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  2. Peter beim Graben
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Correspondence to Stephen Coombes .

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Editors and Affiliations

  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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Coombes, S., beim Graben, P., Potthast, R. (2014). Tutorial on Neural Field Theory. 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_1

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