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Tutorial on Neural Field Theory

In: Neural Fields

Author

Listed:
  • 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
    Deutscher Wetterdienst)

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.

Suggested Citation

  • Stephen Coombes & Peter beim Graben & Roland Potthast, 2014. "Tutorial on Neural Field Theory," Springer Books, in: Stephen Coombes & Peter beim Graben & Roland Potthast & James Wright (ed.), Neural Fields, edition 127, chapter 0, pages 1-43, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-54593-1_1
    DOI: 10.1007/978-3-642-54593-1_1
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