Mathematical neuroscience: from neurons to networks

Coombes, Stephen

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
• 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