Mathematical neuroscience: from neurons to networks

Coombes, Stephen (2015) Mathematical neuroscience: from neurons to networks. In: Actes du colloque "EDP-Normandie" : Le Havre 2015. Fédération Normandie Mathématiques, Caen, pp. 153-160. ISBN 9782954122137

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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.

Item Type: Book Section
Keywords: Neural field models, Turing instability, Interface dynamics
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
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Depositing User: Coombes, Prof Stephen
Date Deposited: 07 Mar 2016 11:15
Last Modified: 14 Sep 2016 11:27

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