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Mathematical neuroscience: from neurons to networks

Coombes, Stephen



Christian Dogbe


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.


Coombes, S. (2015). Mathematical neuroscience: from neurons to networks. In C. Dogbe (Ed.), Actes du colloque "EDP-Normandie" : Le Havre 2015Fédération Normandie Mathématiques

Publication Date Dec 1, 2015
Deposit Date Mar 7, 2016
Peer Reviewed Peer Reviewed
Book Title Actes du colloque "EDP-Normandie" : Le Havre 2015
ISBN 9782954122137
Keywords Neural field models, Turing instability, Interface dynamics
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