Mathematical neuroscience: from neurons to networks
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 i...
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| Format: | Book Section |
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Fédération Normandie Mathématiques
2015
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| Online Access: | https://eprints.nottingham.ac.uk/32112/ |
| _version_ | 1848794337235697664 |
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| author | Coombes, Stephen |
| author2 | Dogbe, Christian |
| author_facet | Dogbe, Christian Coombes, Stephen |
| author_sort | Coombes, Stephen |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:14:35Z |
| format | Book Section |
| id | nottingham-32112 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:14:35Z |
| publishDate | 2015 |
| publisher | Fédération Normandie Mathématiques |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-321122020-05-04T17:20:47Z https://eprints.nottingham.ac.uk/32112/ Mathematical neuroscience: from neurons to networks Coombes, Stephen 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. Fédération Normandie Mathématiques Dogbe, Christian 2015-12-01 Book Section PeerReviewed 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 Neural field models Turing instability Interface dynamics |
| spellingShingle | Neural field models Turing instability Interface dynamics Coombes, Stephen Mathematical neuroscience: from neurons to networks |
| title | Mathematical neuroscience: from neurons to networks |
| title_full | Mathematical neuroscience: from neurons to networks |
| title_fullStr | Mathematical neuroscience: from neurons to networks |
| title_full_unstemmed | Mathematical neuroscience: from neurons to networks |
| title_short | Mathematical neuroscience: from neurons to networks |
| title_sort | mathematical neuroscience: from neurons to networks |
| topic | Neural field models Turing instability Interface dynamics |
| url | https://eprints.nottingham.ac.uk/32112/ |