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
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.
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