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Mathematical neuroscience: from neurons to networks

Coombes, Stephen

Authors



Contributors

Christian Dogbe
Editor

Abstract

The tools of dynamical systems theory are having an increasing impact on our understanding of patterns of neural activity. In this talk I will 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 waves, bumps and patterns, based around natural extensions of those used for local differential equation models. Here I will present an overview of these techniques. Time permitting I will also present recent results on next generation neural field models obtained via a mean field reduction from networks of nonlinear integrate-and-fire neurons.

Publication Date Dec 1, 2015
Peer Reviewed Peer Reviewed
Book Title Actes du colloque "EDP-Normandie" : Le Havre 2015
ISBN 9782954122137
APA6 Citation Coombes, S. (2015). Mathematical neuroscience: from neurons to networks. In C. Dogbe (Ed.), Actes du colloque "EDP-Normandie" : Le Havre 2015Fédération Normandie Mathématiques
Keywords Neural field models, Turing instability, Interface dynamics
Related Public URLs http://edp-normandie3.sciencesconf.org
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
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