Professor STEPHEN COOMBES STEPHEN.COOMBES@NOTTINGHAM.AC.UK
Professor of Applied Mathematics
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.
Citation
Coombes, S. (2015). Mathematical neuroscience: from neurons to networks. In C. Dogbe (Ed.), Actes du colloque "EDP-Normandie" : Le Havre 2015. Fédération Normandie Mathématiques
Publication Date | Dec 1, 2015 |
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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 |
Public URL | https://nottingham-repository.worktribe.com/output/764833 |
Related Public URLs | http://edp-normandie3.sciencesconf.org |
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